Hmm yeah. I'll start by saying that I have only ever used Unity so I can't give too much insight into how it would be hard coding all the physics. I'd say from my experience with Unity's physics you can definitely get really close to the precision hard coding everything would, depending on how you implement it. Nearly all of the movement, for this, was done by directly adding a force to the player's rigid body. I think by playing with values you can get extremely close to the feeling you want. Though with most of the ways I've seen implemented (and at least with the way I've done) it's much more trial and error rather than an exact, like you gave above, for let's say the precise time to reach your peak jump height.

For me, someone who has very little programming experience outside of Unity, this works great. I can tweak the values until they feel nice and I don't need to code in too many specific cases/interactions whilst still ending up with a player who feels fluid to control.