I don't have an answer to your first question; but an observation that may help bring forward more helpful answers by focusing on a particular discipline where formal arguments are made as a kind of case study.
Take physics, here simplicity is often put forward as a key criteria and thus also a kind of mantra to characterise useful ideas and theories and perhaps almost as a way of thought and life; Einstein said a theory should be simple as possible and no simpler, and this is a thought that needs to be unpacked and to be laid out.
Take Maxwells Equations, not as we now find them but as he first wrote them down. Written out fully, they comprise twenty equations - hardly simple; however, when we look in an undergraduate textbook, we find they have been simplified to four equations and when we look at a more advanced textbook, one for graduates, we find only two. (On this evidence one might think that the next step and the last step is to reduce it to a single equation).
What we have here is not simplicity but simplification, and this has been ground out by inspiration and hard work by several generations of collaborative work between physicists and mathematicians.
What then of Maxwells work? It cannot be simple in light of its later simplifications, yet there is something simple in it that has been grasped. Some new reality has made itself manifest even if it remains still uncovered.
Because it is new, it cannot be written down easily in the old forms, hence the complexity of its expression, and the arguments that uncover it; arguments here are complex.
Physics yearns towards the tautological; here truth manifests itself solely as no more than the truth of form, and no less as there is nothing more than form. This is the truth of mathematics where 1+1=2 merely by its form - it cannot be otherwise. (It can become more by being less, to reduce it to the truth of 1, simple in itself - the Pythagorean truth - but this strp is a step towards truth on a symbolic level).
Thus physics, when it looks for its own essences, looks for that expression that comes closest to mathematics, and it's in this uncovering, clearing and motion that simplicity displays itself: to come as close to the tautological without being merely and only tautological as physics partakes of the earth and air in a way that mathematics cannot.