Child seats aren't a problem when riding, probably because their owners rarely, if ever, ride at speeds where they might be become an issue.
IME the biggest issue is when stopped, mounting or dismounting. The child's weight is high and behind the seat, so once you step off the saddle, the bike can twist under you if allowed to lean to either side, and the bars cannot restrain it well once that starts.
There are ways to mange the problem but the rider has to be aware and ready. Whenever any of my family or friends asked about seats, I suggested buying 20#s of potatoes or onions, and riding the sack around for a while so they can get used to and manage the problem. It's far better to dump potatoes on the ground than your own child.
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