The primary reason you shouldn't surrender cognitively is that the truth matters. That's it.
Of course, when you're working on a system of high complexity - and one that is constantly changing to boot - with all sorts of historical reasons and what not that inform the why and so forth, you can't reasonably be expected to understand everything. This is what bracketing is for. When I acknowledge "this is the way X works", it doesn't mean I have to accept the proposition "this is the right way/best way to do X" or "X must be this way". A teacher or mentor may say it is, but in a theoretical context, unless it has been justified, you cannot claim that you know that what has been said is true. However, you can accept it as a provisional working hypothesis. And practically, it may work out and perhaps experience will lend some feeling of substance to the hypothesis, but you needn't make it doctrine.
Empirical science often has the same spirit. Perhaps the model isn't a true account of reality, but it puts handles on reality so that it can be instrumentalized.
There is an occupational danger here. If we focus exclusively on the instrumental, if we reduce all of human attitudes toward the world to use and utility, we not only vulgarize ourselves and our orientation toward the world and even others, but we risk trampling the truth and the good underfoot. We risk developing an indifference to the truth, because all that will matter is some measure of effectiveness. This is what one might call the textbook[0] definition of bullshit.
[0] https://www2.csudh.edu/ccauthen/576f12/frankfurt__harry_-_on...