[Brickcity]

...and Shaw has shown an uncanny preference for playing more experienced quarterbacks even when they are floundering horribly (see: Chryst over Costello circa 2017, especially against Oregon State), it's reasonable to assume that Shaw might have played Burns over Rosen for some time. Sad, but likely true.

I think this story is oversold.

Another way to look at the same events is that Shaw is willing to switch to younger QBs when appropriate.
2012 Nunes wins the starting job, Shaw reaches over upperclassman Nottingham to replace him with unheralded (RS) frosh Hogan.
2016 Burns wins the starting job, Shaw replaces him with (RS) soph Chryst.
2017 Chryst the obvious starter after 2016, Shaw replaces him with Costello.
2020 Shaw ... allows Mills to take over from Costello.

Obviously the complaint is he should have done so sooner.
Would other coaches? Some would have, but not most it seems to me.

None of these cases were remotely equivalent to Rosen walking into a QB room of Jerry Neuheisel, Jake Hall, Mike Fafaul and Craig Myers.
The only time Stanford might have had a similar situation would have been if Mills had shown up completely healthy in 2017, though a QB room of Chryst, Burns, Costello and Richardson was miles away from what Rosen saw.
[And if Rosen had come to Stanford, Shaw would have played Hogan over Rosen when Rosen was a frosh - at least he damn well better have.]

Still, there are cases.
In 2014 not realizing that McCaffrey was the best player on the offense until the last few games is the one that sticks in my craw the most.

I'll answer your question for you. ;-) For the love of God, YES, Shaw should have made those QB switches much earlier than he did. Let's take a look at each of them, shall we?

2012 Nunes was God awful. Other than one quarter against USC and the Arizona game, he didn't play like a D1 QB. How does Shaw not give Nottingham a shot? I have no inside info but have to wonder if there was a personality clash between him and Notthingam. You can also argue that Shaw should have started Hogan a game or two earlier. Either way, having your starting QB repeatedly throw passes at the feat of his receivers is no bueno. 

2016 Burns wins the starting job, Shaw replaces him with (RS) soph Chryst. 
Beginning with the UW game, Burns did not play like a Pac-12 level QB. It's true that he played against the much easier part of the schedule so it's possible that Chryst might have been no better. So, I'll give Shaw the benefit of the doubt on this one. 
2017 Chryst the obvious starter after 2016, Shaw replaces him with Costello. 
Chryst deserved to start the 2017 as the starting QB. But, he crapped the bed big time against SDSU (I was at that game and it was truly a pathetic performance.) Then, he follows up that masterpiece with arguably an even worse performance against UCLA. A game we would have lost by multiple TDs had he not gotten hurt. Costello comes in and we end up blowing out them. I'd argue that a good coach - that is, one who prioritizes winning (and really, isn't that one of the main criteria of a "good coach") would have kept Costello the starter for the remainder of the year. Once Chryst returns from injury, Shaw holds a sham of a "QB competition" where I think we all knew who would win out, though undeservedly. After Chryst "wins" the competition, he has his true masterpiece of a season in which he makes Josh Nunes look like the second-coming of Andrew Luck: against OSU, I saw one of the worst QB performances I'd ever seen in my life...among any QB at any level. At halftime, Shaw STILL refuses to make the QB change. Even the announcers were perplexed. Had Harrison Phillips not made the play of a lifetime by getting the strip and fumble recovery, Stanford loses that game. This was the moment that I realized that Shaw cares less about winning than he does preserving some weird, artificial pecking order among his QBs. 
2020 Shaw ... allows Mills to take over from Costello. 
I don't know what Shaw said (or didn't say) to Costello after the season concluded, so I don't have a strong opinion on this one. 

Bottom line: Shaw just is not that competitive. Sorry, but true.

[Brickcity]

...and Shaw has shown an uncanny preference for playing more experienced quarterbacks even when they are floundering horribly (see: Chryst over Costello circa 2017, especially against Oregon State), it's reasonable to assume that Shaw might have played Burns over Rosen for some time. Sad, but likely true.

I think this story is oversold.

Another way to look at the same events is that Shaw is willing to switch to younger QBs when appropriate.
2012 Nunes wins the starting job, Shaw reaches over upperclassman Nottingham to replace him with unheralded (RS) frosh Hogan.
2016 Burns wins the starting job, Shaw replaces him with (RS) soph Chryst.
2017 Chryst the obvious starter after 2016, Shaw replaces him with Costello.
2020 Shaw ... allows Mills to take over from Costello.

Obviously the complaint is he should have done so sooner.
Would other coaches? Some would have, but not most it seems to me.

None of these cases were remotely equivalent to Rosen walking into a QB room of Jerry Neuheisel, Jake Hall, Mike Fafaul and Craig Myers.
The only time Stanford might have had a similar situation would have been if Mills had shown up completely healthy in 2017, though a QB room of Chryst, Burns, Costello and Richardson was miles away from what Rosen saw.
[And if Rosen had come to Stanford, Shaw would have played Hogan over Rosen when Rosen was a frosh - at least he damn well better have.]

Still, there are cases.
In 2014 not realizing that McCaffrey was the best player on the offense until the last few games is the one that sticks in my craw the most.

I'll answer your question for you. ;-) For the love of God, YES, Shaw should have made those QB switches much earlier than he did. Let's take a look at each of them, shall we?

2012 Nunes was God awful. Other than one quarter against USC and the Arizona game, he didn't play like a D1 QB. How does Shaw not give Nottingham a shot? I have no inside info but have to wonder if there was a personality clash between him and Notthingam. You can also argue that Shaw should have started Hogan a game or two earlier. Either way, having your starting QB repeatedly throw passes at the feat of his receivers is no bueno. 

2016 Burns wins the starting job, Shaw replaces him with (RS) soph Chryst. 
Beginning with the UW game, Burns did not play like a Pac-12 level QB. It's true that he played against the much easier part of the schedule so it's possible that Chryst might have been no better. So, I'll give Shaw the benefit of the doubt on this one. 
2017 Chryst the obvious starter after 2016, Shaw replaces him with Costello. 
Chryst deserved to start the 2017 as the starting QB. But, he crapped the bed big time against SDSU (I was at that game and it was truly a pathetic performance.) Then, he follows up that masterpiece with arguably an even worse performance against UCLA. A game we would have lost by multiple TDs had he not gotten hurt. Costello comes in and we end up blowing out them. I'd argue that a good coach - that is, one who prioritizes winning (and really, isn't that one of the main criteria of a "good coach") would have kept Costello the starter for the remainder of the year. Once Chryst returns from injury, Shaw holds a sham of a "QB competition" where I think we all knew who would win out, though undeservedly. After Chryst "wins" the competition, he has his true masterpiece of a season in which he makes Josh Nunes look like the second-coming of Andrew Luck: against OSU, I saw one of the worst QB performances I'd ever seen in my life...among any QB at any level. At halftime, Shaw STILL refuses to make the QB change. Even the announcers were perplexed. Had Harrison Phillips not made the play of a lifetime by getting the strip and fumble recovery, Stanford loses that game. This was the moment that I realized that Shaw cares less about winning than he does preserving some weird, artificial pecking order among his QBs. 
2020 Shaw ... allows Mills to take over from Costello. 
I don't know what Shaw said (or didn't say) to Costello after the season concluded, so I don't have a strong opinion on this one. 

Bottom line: Shaw just is not that competitive. Sorry, but true.