I understand the worries about loading and unloading a child seat on a bike. I've experienced those difficulties many times with several kids, as well as the differences in bike handling. (Admittedly, these experiences were on standard, non-folding bikes, including our tandem, but not on Fridays.)
But as a practical matter, telling most couples that they should not use a kid seat is telling them to stop most of their bicycling until their kid grows. Certainly, as a young married couple, we lacked the money to buy a new and unusual bicycle just for carrying a kid. Instead, we used care to stabilize the bike
for loading and unloading
(usually by locking the front wheel and leaning it on a wall, with one parent holding it). And of course I was very careful when riding, as I imagine almost all parents would be.
I never experienced even a close call that way, which is of course anecdotal information; but if kid-seat crashes were a serious problem, I'd think they would appear in data somewhere. Despite decades as a "data head" with a passionate interest in bike safety, I've never encountered such data. Does such data exist, or are people merely imagining a minuscule problem, another "bicycling is dangerous" variant?
Oh, and speaking of anecdotes: I clearly remember when one of the first local couples to use a kid trailer flipped the trailer and kid while making a sharp turn, when the inside wheel hit the curb. Nothing is without risk.
Finally, I believe a bike is more stable overall when a heavy load is on the front wheel, directly controlled by the handlebars, instead of on the rear wheel. I've thought about, but never tried, touring with a tall backpack (e.g. Rick Steves Bag) fastened to a Friday's handlebars and a low rack just over the front wheel. I wonder if a kid seat mounted low and in front might be best.