Had this same situation many times. I always allow them to tag my luggage, take it down the jetway for the valet check and remove the tag before getting onto the plane luggage in hand.
I love the creative non-compliance.
As mentioned earlier, PSA requires anything with wheels to be checked.
Generally speaking matches my experience on American Eagle CR7's. Although I need to include a Dated Content Alert I have not been on one in quite some time. Not seeing nearly as many at DFW as we used to.
It's been over a year since I flew a CRJ700 but IME anything larger than your personal item was valet checked, which is different from gate checked. . . . . . while valet check means you pick up your bag airside when your flight lands. . . . . . on the jetway.
I've been valet checked many times on AA Eagle RJ's. Which is a low care-o-meter thing that is not worth getting into it with a GA over. I presume but do not know that was what was going to transpire. Now if people are getting bags taken and thrown into the hold rather than red tagged and given back at the gate that would be news.
If anything I haven't seen nearly the level of mass fine-tooth bag sizing that was once common for anything smaller than a apparently-oversized walrus of a bag in quite some time. Meaning I have also now probably jinxed all of us to a painful interaction with a low-seniority GA wearing rubber gloves and wielding a cheap tape measure. Who is being forced against their will to work overtime for duration of the holidays, and isn't happy about it.
(Speaking of which; has the woman at LaGuardia that more or less fit that description, but all the time, finally retired)? My NY flying has cut way, way back. But I haven't seen
looped around the back side to avoid her in a long time).