I'll take a stab at an explanation for the first, which will also shed some light on why I lean toward suspecting the second, but I'm not familiar enough with current academic philosophy to make such a conclusion in general.

The main thing that math has going for it is a language that is very different from ordinary natural languages. Yes, terms from various natural languages are borrowed, and often given very specific mathematical definitions that don't (can't if they are to be precise) correspond exactly to ordinary senses of the terms. But the general language contains many obvious markers that say "this is not an ordinary english(or whatever) sentence" even when a mathematical proof contains english sentences.

On the other hand, a philosophical treatise, reads like a book. A regular book in an ordinary natural language, language which we are accustomed to understanding in ways that include letting ambiguity and metaphor give it extra depths of meaning.

Natural language just doesn't map to formalism well at all. Trying to discuss anything purely formal without using a very specific language which contains big bold markers of rigor and formalism (as math does) is very likely to lead to a bunch of category errors and other subtle reasoning problems.

Seconding, though I originally meant the second question. I am also not sure whether you are referring to "conceptual analysis" (then the second question would be clear to me) or "nailing down a proper (more proper) definition before arguing about something" (then it would not).