Chaosmancer
Legend
No, it won't come up every combat.
Because resources are finite and not every combat will present a situation where you want to burn both in the same round.
You start with two Inspiration. For 6-8 encounters per day. At 7th that goes to per Short Rest and you have reached what, three Inspiration? So that's still not often. It'd have to be a hell of a round to make burning two make sense.
Most other subclasses don't have the same sort of issue, though some do have a problem with the Inspiration not sticking around.
You realize that doesn't make the situation any better, and in fact worse right? This is another thing I strongly dislike about the current iteration, the bardic inspiration has been drastically cut and with Fount moving to 7th, it will be even longer until it feels like you can use it outside of "emergencies".
And is that emergency going to be turning a failed save into a success, or a hit into a miss? Those are both fundamentally useful things, but it is going to take 50% of the bard's resources to do one, and they cannot prep another character to succeed, and then use their cutting words to protect a second. I do like it being a reaction meaning that it can't be forgotten or wasted, but I think there are some massive restrictions that came along with both abilities being reactions.