This is one of the oldest recurring requests.
If this gets any traction, we're going to see it anyway so let's just get it out of the way right now; "The technology just isn't there yet." - Riot
Long story short, the ability to change rune page setups in champ select would be a great thing but should not be something we expect to happen any time soon.
I would love for this change to happen but let's face it, if it could be done, it probably would've been done by now especially with all the focus on strategic gameplay/diversity/etc.
It is possible that Riot simply doesn't want to do it. Rune page customization in champ select could cause problems or bring other problems to the forefront.
Pre-game surprises are less impactful
Right now, it is common for people have custom rune pages for specific champions (meta-picks or personal favourites) and a bunch of general purpose ones.
Even if you or a professional player were in Draft Pick and you can see cheese on the enemy team, you cannot truly prepare for it because you are only able to change your masteries.
Because of this, it is useful for players and teams to have 'pocket picks' and cheese strats.
You don't see rune setups being highlighted in LCS during loading screens nor do commentators mention it unless somebody is using something that isn't the 'standard'.
Rune balance
Some runes and setups are just plain better than others. I'm not talking about usefulness, I'm talking about statistics.
Generally, 1 Quint = 3 Primary runes; or at least this was supposed to be the case. As things stand now, rune balance is shit and it is possible to have 'wrong' or 'sub-par' setups because of inconsistencies.
Consider some of the most common pick ups:
Flat AD Red = 0.95 AD; Quint = 2.25 AD; Quint is only worth ~2.37 Reds.
Flat AP Blue = 1.19 AP; Quint = 4.95 AP; Quint is worth ~4.16 Blues.
Flat AS Red = 1.7%; Quint = 4.5%; Quint is only worth ~2.65 Reds.
Flat CDR Blue = 0.83%; Quint = 2.5%; Quint is worth ~3.01 (0.01 flat value difference)
Flat AR Yellow = 0.9 AR; Quint = 4.26 AR; Quint is worth ~4.73 Yellows.
Flat MR Blue = 1.34 MR; Quint = 4 MR; Quint is worth ~2.99 Blues (0.02 flat value difference).
Once you learn the intricacies, you'll understand why some of the 'standard' setups are the way they are.
For example, you would use [x6 CDR Blues] over [x2 CDR Quints] for [5% CDR] so that you can abuse higher value Quints (like Flat AP) while still having 3 blue slots to spare for an extra [3.6 AP], [4 MR], or to bump your [Magic Pen from 7.8 to 9.8] for flat Mpen and [5.49 to 7.38] for hybrid Pen.
The ability to change rune page setups in champ select should definitely be a thing.
But then again, so should a lot of things. Like...
Champion stats and stat gain consistency based on role + ability functions should be a thing.
Chromas for IP should be a thing.
Skin Roulette for IP should be a thing.
XP conversion to IP upon hitting level 30 should be a thing.
Replays should also be a thing.
Sandbox mode should be a thing.
Tournament spectating should be a thing.
Opt-in voice comms should be a thing.
Actually useful tutorials should be a thing.
Mentoring should be thing.
Champ select lobby disband votes should be a thing.
So the point here is:
a) good on you for bringing this up
b) don't expect anything to come out of it
c) yea, this is frustrating but don't dwell on it too much
I found a video from Phreak that goes through his Season 5 rune pages, and I think if you use these, you could find a page that works in almost every situation. Rito pls notice this thread... Only you can make this happen 
