The same problem that guns designed to run with suppressors have when they aren't mounted, or how some companies have oversized gas ports in the .090 range. Especially with lighter buffers. Massive overgassing.
If bad enough, it won't strip the next round from the mag or lock back on an empty because it's causing the bolt group to move to fast.
If it runs, eventually the trigger and hammer pins can break and the holes in the receiver will get out of round... this is the more common reason lowers get out of round trigger and hammer pin holes. Not from the pins rotating, but because the bolt is coming back so hard that it's slamming the fire control group much harder than it should be and that force is being transmitted to the receiver. Another reason I don't like the anti-roll pins... they can actually mask a bigger problem, and will do nothing to help this specific situation.
Parts will wear out much faster. The bolt will break sooner... it's already the reason that carbine bolts don't last as long as rifle bolts. They have a higher incidence of breaking lugs, or at the cam pin hole than the ones in rifles.