The vast majority of use-cases I can think of are simply allowing you to line up the first letter of a line, or possibly an equals sign or something like that. This seems like something a tab-stop or somesuch in the editor could handle with ease, and shouldn't require sacrificing nice-looking text the rest of the time.
In fact, my editor of choice (Vim) assumes in many places that all displayed characters have the same width; it makes it a more consistent experience and allows you to do things on a simple console that you'd normally have to draw a complex (non-portable) GUI for.
But yeah, I can think of a few people who AFAIK do mostly use proportional fonts, and they do just fine. I think it's mainly a path-of-least-resistance thing.
The drawbacks were things like confusing lowercase L with 1 (one) in the sans-serif font I preferred, or the sort of editing where I was trying to change stuff at, say, character position 67 in a series of lines. It seems better for writing code than for editing it. Definitely give it a try if you haven't yet.
A lot of people rail against tabs; most of the time, these are people who don't understand them or have never tried to use them.
You see this debate about tabs vs. spaces in code all the time, and I've yet to hear any valid argument about why spaces are better (at least in any modern context). But there is an obvious reason that tabs are better: It's much easier to line things up, keep them aligned across different users' fonts, and realign them if you change the text to cross a tab.
I don't use tabs because of an equally obvious reason that spaces are better: because I end up padding with spaces because the tabs are too big. For example, I like having horizontally consistent parameter argument lists, like below:
class Thing {
def beep(bar: String, baz: Int, quux: Seq[String],
quuux: Map[String, String], quuuux: Int) = false
}
(Plus, my editor treats four spaces in a row as a soft tab anyway, so I don't even notice it except when I want to. Life is peachy.)
You can still achieve what you want, and even faster, by using tabs to get your subsequent parameter lines most of the way there and then padding with a couple of spaces.