If the difference between reality and approximation is too small to measure, would you even be able to distinguish the two? If not, then we're arguing over nothing, but if so, it hardly makes a difference because whether it's 1100 K or 1115 K, the engine in your car continues to function normally.
Assumptions such as incompressible or inviscid are useful; if they weren't, we wouldn't use them. In fact, there are many instances where we don't use them. Non-dimensional analysis will tell you what assumptions are reasonable to make, and if you're completely intolerant of assumptions for whatever reason, there are other more complete equations that do not make those assumptions. They're just notoriously difficult to solve without using numerical methods.
To the OP, if you're interested in learning more about the sciences, I would start with /literally anything but/ Fluid Mechanics.