I didn't know physics problems are assumed to be idealized... When you build a bridge for example, will the physics try to be simplified to the max? (Honest question here).

Velocity would matter -- it seems to me -- if there is friction and probably a few other factors included like elasticity. No?

Personally, I always considered physicists to be applied mathematicians (not the other way around although I've seen physics problems thrown in university level math classes). That's why I put that there, so assuming a high level of math skills, you'd probably change your way of thinking quite a bit.

When you build a bridge, that's engineering, not physics. It's a physics convention that unspecified factors are assumed to be unimportant. If they were important, they would be specified.

Anyway, it's implausible that the elasticity of the rope or the friction of the pulleys are going to matter. Unless you have really rusty pulleys, or something.