Why is it okay to write a framework of physics by neglecting time itself in favour of a simple model? (question on electrostatics)

The absence of time implies a lot about even the ideal universe the theoretical framework lives in. Because I'd think that Time is a very important measuring tool in calculating the motion of an object.

(Velocity = Distance/Time)

And, to completely dismiss this measuring tool in a frame-work? Aren't we the ones who assigned it as a fundamental quantity in which we use to scale other quantities? The choice feels odd to me- Yes, The goal seems to be figuring out patterns of static electric phenomena. But the notion of static-electric phenomena is so foreign to me- I can't grasp the concept of just taking t=0 for all cases.

What would that even mean, Where in the world would we find roughly approximately equivalent systems to apply our ideas?

And to make my confusion worse, I regularly come across electrostatics problems where time is a quanitity that exists. Even if it's really small- It should still be somewhat of a time-period shouldn't it?

For example, From my textbook: (You do not have to solve this) "An electron falls through a distance of 1.5 cm in a uniform electric field of magnitude 2.0 x 10^4 N/C. The direction of the field is reversed keeping its magnitude unchanged and a proton falls through the same distance. Compute the time of fall in each case. Contrast the situation with that of 'free fall under gravity'".

CORRECT ME IF I'M WRONG BUT WOULDN'T THE MOTION OF THE ELECTRON AND PROTON REQUIRE TIME TO EXIST?? HOWEVER SHORT THE TIME PERIOD MAY BE?? WHY ARE WE SO COMFORTABLE COMPLETELY IGNORING IT???

Forgive me if the question sounds stupid, I'm a highschool student whose head falls into the most meaningless arguments in the midst of studying. Someone please exorcise this horrendous itch.