Broom-spells are cast long before the rider gets on.

Yes, you’re right, the analogy was not correct. But my point is that it appears that the broom spell does what’s intuitive, and the transfiguration spell apparently does not.

think if nobody warned about the dangers of transfiguration there wouldn't be any issues?

No, in MoRverse at least people would die. But that’s my point, it’s weird that you need dire warnings that transfiguration doesn’t work as you might expect, but pretty much every other spell we’ve seen does not require such warnings, even if very powerful (e.g., time-turners; note that Harry was terrified, and Minerva acted less concerned than if she gave him a bike).

shallow expectations don't seem to have much of an effect on transfiguration

Exactly. Why do they seem to have an effect in other cases?

For example, a teleport spell will also have to compensate for the difference in velocity between the departure and destination. But the shallow expectation is that you’ll arrive stationary, and it works as you expect. Also, it takes with you whatever you’re wearing, even in a pocket, and presumably even if you don’t know you have it on you, but doesn’t take the carpet you’re standing on (and so do time-turners).

Aresto Momentum itself looks very safe on first view, and nobody warns about, say, casting it while inside a moving vehicle (depending on what it actually means, which if you think hard about it is not very clear, it should be very dangerous to cast it on objects inside or outside the vehicle).

Time turners don’t drop you in outer space. Brooms partly ignore inertia. Tooth-growing charms don’t break your jaw. Accio doesn’t seem to kill people or destroy property, even if you summon an object from very far away, and doesn’t work on buildings. Fold-space objects have limited capacity, but one can enter a space-folding trunk while holding a space-folding pouch without needing to think about the possible consequences. Floo powder protects you not only from the burning, but also from suffocation and CO poisoning (you keep your head in the fire to use it for communication).

Even accidents are somewhat intuitive: an extra cat hair in Polyjuice can give you cat attributes instead of blowing up or not working at all. Varying pronunciation varies the kind of bats you can summon, but all variations are benign (e.g., it makes green-glowing bats instead of X-ray–glowing bats).

It’s not obvious why the same does not happen with transfiguration. (One might expect that if you break the transfigured object, the original might be broken, but movement of molecules in what appears to be a solid is not intuitive.)

What’s even weirder is that if you think even deeper about it, it should be much worse. For example, if you transform something into a liquid, the original should probably disintegrate completely. But Minerva’s desk looks normal, even though almost 10% of the pig (the blood) is completely shuffled. (Also, if you can make a pig, and you can transfigure a person (dangerously), you should be able to transfigure a dozen stones into a dozen copies of yourself. The copies are doomed, of course, but it’s still weird nobody ever made a temporary army of themselves.)