This is a personal question, no "right" or "wrong" answers. I think MMM keeps things as simple as possible, and he doesn't budget. If he should buy something he does, if he shouldn't he doesn't. How much money is in the bank isn't a factor because there is always money in the bank or available as needed. There are bigger picture principles making the decision than a "budget". So I don't think of budgeting as a "mustachian" way of spending, it's a crutch (very important and helpful crutch) on the path to becoming mustachian.
So that is the way I am heading, I have been closing accounts from our early days of budgeting by having multiple accounts. But having the multiple accounts was a huge benefit right in the beginning. We needed a strict framework to force us into new habits and new thinking, so we had monthly budgets going to various accounts which we moved money between. It forced savings in some areas, but more importantly it forced us to consciously think about our spending. The automatic transfers were not hard to set up, and are not hard to change, so if you want to try it there is no big down side. I use Capital One 360 but there are many good banks, just be sure they have a good web interface for working with.
Right now we are dropping accounts, and we are down to just a few. Things like clothing are so rare, and I never think about the "budget" anymore when buying clothing, we are no longer tempted to spend on clothing that isn't needed or have the right priorities behind it. We don't have an "emergency" account, we have a HELOC that would be fine, and have other savings that could be used if needed. For example, there is a remodel fund that we are saving up to spend this summer, and there is a vehicle fund that pays for maintenance and future vehicle purchases. My wife and I each have small discretionary accounts that we each use in our own way, but that is just us, not every marriage works the same way obviously.
So if multiple accounts work well and helps great, but I don't consider it mustachian to have multiple accounts, keeping it really simple and having it earning money for you is mustachian.