I'll agree with others here that there's no guarantee that there will be room for your carry-on. But since there were later flights that day available, and OP was willing to be moved to one, that's the reasonable and logical solution.

(That's not very game-able, few passengers would want to schlep out to the airport, wait for boarding, for the "benefit" of a free rebooking to a flight a few hours later. )

I wonder what would have happened if you explained that your carry-on was full of spare lithium batteries?