Intentionally "Bugging" Game for Profit
Maybe the reason changing runes in champion select is so bugged is because rune pages used to be a huge profit for RIOT. Being able to switch rune pages but not individual runes for a period this long has undoubtedly lead some people to give in and buy a few more pages (if not a bundle).
Which meaans not being able to change your runes is profitable. RIOT can't admit they made a financial mistake by allowing on the fly rune changes, and this "bug" is their way reconciling their losses. I even considered buying a bundle myself until I realized how easy it would be for them to fix this issue.
The last 3 games it happened to me was simply a matter of the rune page popping up behind the champion with the "X" to close being visible. Since this never happened when rune pages were in high demand, I have no choice but to believe this "bug" was implemented intentionally for revenue.