Using assumptions to clarify complex problems is hardly non-scientific. I don’t understand your point. The goal is to get as close as possible, there is always a margin of error. There is no “scientific truth” to FEA. Materials always have flaws, defects, cracks, etc… depending on the analysis changes whether those need to be considered of if they can be covered with a safety factor.
I use a minimum SF of 1.1 for most body calculations, 1.25 when considering different materials, and 1.32 when dealing with gas. If the hand calcs (done in a massive spreadsheet but more or less normal burst calcs) go below the safety factor FEA is performed to analyze the assumptions in more detail. We use the assumptions so you can easily identify if the part is close to a weak point or not. Not going to waste the time on FEA if the part has a SF of 3.
My point is that understanding the flaws of nature is hardly un-scientific and modern engineering is extremely science driven. I cannot use real world experience and the common “that’s the way its always been done” excuse to account for flawed designs. That is how you lose business. You have to back it up with scientific analysis, which is what a good engineer does.