Nothing like having a crushing defeat round 1 then 50-80% of demoralized team quitting and having the opposing team then bullrush through all the objectives before the "balancing" has time to plunk one person over—crippling the pacing of a match that could be easily salvaged with a balance in players.
I don't think that goes far enough though. There needs to be some heuristics to account for player rank when balancing (since map knowledge is probably the single-most important advantage in such a lethal game), limit the amount of "balancing" of any single player (high scoring players tend to get swapped back and forth multiple times, losing plenty of playtime), account for the sole defender or attacker on an objective as to not spoil critical moments, and in general avoid swapping "living" players.
Maybe apply some weight system to all players on aforementioned and additional factors, then during balancing countdown wait for the most weighted player(s) to die to swap, or some "idle" movement threshold (outside of any objective), or if any one player's weight is grossly exceeding all others than maybe a last-resort mid-action swap.
I'm not sure if any such measures have already been put in place; I haven't had the frequency in gametime or active observation, but historically the "balancing" system has been lacking in satisfaction. The OP is definitely the most noticeable of its flaws though.
Until there's effective infrastructure for a competitive scene, PUGs will continue to get slogged by groups on a team retaining full roster while the other rage-quit before waiting for the slow decay that is the current "balancing". Hell, that might be the only time where unbalanced team sizes would be fair—short-roster groups vs full-roster PUGs.