That's a big part of it. Distortion does two big things to your tone; it adds presence and treble artifacts from squaring waves, and it loses bass, because the peak levels of your fundamental bass frequency are getting limited/compressed by the clipping. A wet-dry blend gives you back some of that low end, while post-clipping tone controls will give you more ability to roll back the fuzzy aggressive highs.
Plenty have bassists have done so before. The only problem you're going to have is that tone-shaping to make the fuzz sound good is going to do funny things to your clean tone when you turn the fuzz off. I recommend that if you're going to use the Big Muff you have, you look for an EQ pedal that you can turn on and off with the fuzz, so the more extreme tone-shaping you do to control the fuzz with the EQ doesn't affect your clean tone.
The advantage of a pedal like the DBBMP, Alpha-Omega Ultra, Microtubes Ultra etc. is that you get everything you need to craft your dirt tone in one enclosure, with one power input, one input/output and one switch to turn it on and off, simplifying your pedal board. But, there's a value in the modular approach as well, being able to choose the specific dirt and EQ circuits you want to use instead of accepting whatever someone mashed together (not to mention using things you already have instead of buying them again in a different enclosure).
Whatever you decide, don't worry too much about getting an XLR out and not using it. The DBBMP has one, I don't use it and I don't feel I wasted my money. Little trade secret, an impedance-balanced XLR out is really cheap to make and therefore to include in an effects pedal as a "value-added" thing. They are cool to have handy, but if you end up not needing it, don't sweat it.
