Maybe give your daughter a break on a first DM and not break out the counterspells, and let her enjoy the experience of lobbing some fireballs at your PC? Does it really matter if you can’t counterspell.
Injecting ambiguity where there wasn't before is rarely a good way to go (especially if there is a better way).
As @Blue stated - the problem could go beyond counterspell. Off the top of my head: Ancient Paladin's 7th level aura and the spell Globe of Invulnerability suddenly become less useful - or more ambiguous.
Is it easy to rule around? Perhaps, but that doesn't mean it's not irritating.
Further, the whole goal seams to be to make monsters more streamlined and easy to run (especially for first time players) which is a GREAT goal. but it's worth exploring unintended consequences to make sure that goal is actually accomplished.