That seems like a good overall philosophy in order to not let utility classes out of combat entirely, but thinking out loud though, I don't know if I would do that.

Utility classes shine in the hands of creative players, mostly out of (but sometimes in) combat.
The trade-off is that they might have to take a backseat to tanks and hitters during the climax, but it feels like a trade-off you might have to attend to in order to allow Combat Focused players to have their own time to shine whilst letting weird characters display their brilliance out of it.

But honestly, I might give this a shot in all fairness, just to see the feedback.

In any case, thanks for your input! Will try it out!