That's what MUNI is. It started as hundreds of independent railways crisscrossing the city. They slowly unified them into the cacophony that is MUNI.
I say cacophony because there are bus', cable cars, vintage light rail, modern light rail, subway, tram, local neighborhood shuttles, and I'm sure I'm missing a few.
Well yeah, that's what a modern public transportation system looks like - I know that's unusual in the US, but if you look at other places, e.g. Europe, you will also have buses, trams/light rail (with tunnel segments and heritage services for tourists) and minibuses/neighborhood shuttles in most bigger cities. The only thing that sets SF apart is the cable cars - and having both a fully grade-separated metro (BART) and a light rail system with tunnel sections (Muni Metro) - usually in cities with a "full metro" the light rail is a tram without tunnel stations.
I mean, Montréal also regularly sees temperatures around -30 C in the winter, so it's not completely ridiculous to suggest this decision may be informed by fundamentally different design constraints from, say, San Francisco or many European cities [1].
You can do covered at grade (e.g. Sofia Metro has a few km section like this - covered to protect against the cold weather in the winter, but at grade to save costs).
Montreal did it wrong so nobody should try again? I'm struggling to see what your point is. Montreal is in north America, not Europe, in case you're not aware.
I say cacophony because there are bus', cable cars, vintage light rail, modern light rail, subway, tram, local neighborhood shuttles, and I'm sure I'm missing a few.