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Just as you can respect a program more for winning NCs under several different HCs, I think the reverse should be true of HCs winning at several different programs.
You could look solely at NCs, if you want...I guess.
But then HCs like Bill Snyder and yes, Bo Schembechler are invisible to you.  Odd.

Spurrier won at 3 different programs, none of which had any history of winning.
He led Duke to their first ACC championship since 1962 (27 years). 
He led Florida to our first ever official SEC championship.  Then won 5 more.  And finished 1st in the SEC his first year, but we weren't eligible.
He is South Carolina's all-time winningest HC, and it's not close.
He is Florida's all-time winningest HC, and it's even a wider gap. 
Despite Meyer's three 13-1 seasons and despite coaching twice as many seasons at Florida as Meyer, Spurrier's win% is higher.  That's nuts.
Part of that is while he was the HC (OBC) at Florida for 12 seasons, he lost 12 SEC games.  Total.  He dragged the SEC into the 21st century, no longer considering 3 runs and a punt as success.

Here's a list of most season wins for South Carolina, all-time:
12, 12, 12, 10, 9, 9, 8, 8, 8, 8,...
Spurrier is all three 12s and a 9.....4 of the top 5, ever.

Yes, he was sub-.500 vs FSU, but Florida at that time had a unique and unprecedented end to its seasons.  Top-5 rival, then conf championship game, then as a top-10 team itself, a bowl vs a legit top-10 opponent.  No one else had that.  Tennessee ended the year with Vandy.  Georgia ended it with GT.  UM-OSU played each other in the finale, but no CCG.  Nebraska didn't have a CCG until they did, and their run ended around that time, coinciding with Dr. Tom's exit.

Anyway, any great HC can be talked up by a fan of his program. 
I value consistency.  Osborne's million straight years with 9+ wins is insane.  Bowden's 14 straight top 5s is nuts.  Bo only losing 24 Big Ten games in 21 seasons is nonsense.
And as we all know, pre-playoff, winning the NC was as much luck as anything else.  When you lost.  When someone else lost.  Hell, going undefeated and not getting even a piece ('94 PSU, '04 Aub).  So I don't like the idea of Spurrier is amazing and Bo was not, just because Texas upset Nebraska and we got a rematch with FSU. 

When a HC is an all-time great AND fun, it's just a special time.  Visor-throwing, poking shots at opponents, trying to hang 50 on everyone and often doing it...that's why Gators love Spurrier most.  Meyer won 2 NCs, but Spurrier won our first and we all had fun as it happened. 

Spurrier could absolutely be on someone's College HC Mt Rushmore....but so could 20 other guys.

I'm not certain if you're directing that comment I bolded up above at me or not.  But I very much respect Bill Snyder, by all accounts he did very, very well at KSU.  And I do think it's unfair to not include him just because he never won a MNC, but on that list of great coaches the only other one who never won a MNC was Bo Schembechler.  And it's always a knock on him as well. 

I honestly don't really know much about Bo, he was done coaching long before I took an interest, and I still don't pay that much attention to the B1G or many of the coaches in general.  Michigan always gets an outsized amount of coverage, and so does Ohio State, but I don't really know much about their programs from before the late 90's.  

So if you wanted my Top Ten, I'd probably include Bill Snyder, as well as Stoops, Bowden, Spurrier, Saban, Miles, Mack Brown.  Not sure who the other few coaches would be, I haven't given it a lot of thought. Notice how my list only includes coach from the last ~30 years?  It's because that's as far as my CFB fandom goes.  Anything before that is ancient history.  

Bill Snyder taking Kansas State, one of the ends-blown-out tomato cans that Nebraska and OU feasted on in the historical Big 8, to the fringe of a MNC, and then keeping them there for a while, is worth being in the discussion of Rushmore.

That LSU team is such an interesting case study.

They were super accomplished, beating a ton of very good teams (even if the 8 ranked teams thing is a bit hollow). Their defense was murder. Their offense was … quite good, not unreal. Held under 4 yards per carry almost half the time, under 5.7 yards per play more than half the time.

And that would’ve been fine, if not for facing maybe the most talented defense of all time. I rather hoped LSU could’ve locked down that amazing accomplishment of a season. But they didn’t.

It’s too bad, but the sport doesn’t always deliver the best story (and of course that game and mulligan choice was the first playoff breaking point)

That LSU offense was "efficient,".....good at what they did (running the ball), but extraordinarily limited.  I don't know what 'fro is on about....those QBs were both awful, in quantifiable numbers and in QB skillset.  You can't watch either of them that year and honestly say "that's a game manager."  No, with a "game manager" they'd have won the NC.  He's right that they didn't need to throw the ball much, but that doesn't change the fact that they were crap at reading coverages and pulling the trigger when they did need to.  

I'll go to my grave haunted by the memory of TEs streaking uncovered down the sideline and wide open crossing routes, and a QB who was so bad he instead shovel-passed the ball directly to a guy wearing the other color.  

Bill Snyder taking Kansas State, one of the ends-blown-out tomato cans that Nebraska and OU feasted on in the historical Big 8, to the fringe of a MNC, and then keeping them there for a while, is worth being in the discussion of Rushmore.

This is always an odd one. 

We’re talking about a guy who took a 10th percentile power team to consistent 80th percentile, and sometimes 90th+. Thats awesome. 

For better or worse, guys who can take a team from 80th or 90th to 100th get the top-end hype. And it’s just kind of different skillsets. Like, it’s all coaching, but what Snyder did was so underdog, it doesn’t really apply to what Saban did (and as we saw, the load up on talent at a mid-tier program thing was far from dominant for Nick).