Your "b" is what you think I did, and it isn't correct. The purpose of simplifying assumptions is always the same and does not hinge on the effect being negligible. As the name suggests, the purpose is to make a problem easier to solve (isolate an effect you want to examine) by ignoring other effects you don't care about. Again, this is done all the time, particularly in Relativity threads, where impossible scenarios are proposed a dozen times a day.OK
There is a difference between:
a) Making predictions, while ignoring aspects that have negligible quantitative effect on the result.
b) Trying to prove something, based on a set of mutually contradictory assumptions
I'll be specific:
1. In the "barn door/ladder paradox", to make this thought experiment physically real requires closing the barn doors instantly and a signal receipt, processing and response system that acts instantly. That violates Newton's laws of motion and SR.
2. In the twins paradox, accelerations are assumed instantaneous, also in violation of Newton's laws and SR.