That is, it does unless you actually like stepping over homeless people and being mugged.
We have a 1300sqft house in HCOL and it still has a bunch of unused space; we used to have the same problem even in a 1100ft apartment. My friends have a cheaper big house a 40-minute drive away; the reason they have a big house is because they want to be near certain outdoor activities, and there are no small houses in that area. Half the house is literally unfurnished, nobody ever goes there.
Come think of it, my two main problems with my house is that (1) it's too long of a walk to a bus (like, 7 minutes) and bars/etc. (like, whole 5-15 minutes); (2) (didn't affect us directly yet) heroin addicts stealing stuff. Both of those would be worse in a typical LCOL where I could afford a McMansion I wouldn't bother fully furnishing.
I'm not in BA and I think BA is vastly inferior to where I'm at, but for me an apartment in BA >> a 4000sqft house in rural Kansas. It's like, not even on the same level. Judging by the prices, many people agree :P
Nobody wants to take the bus. It doesn't run 24x7. It doesn't go direct, door to door. At the beginning and end of the trip, nobody wants to walk 7 minutes in unpredictable weather while lugging a bunch of stuff. Nobody wants to endure a slow trip, stopping every couple blocks, with a couple bus changes that take a half hour each. Before you get your groceries home, either your ice cream melts or your hot chicken gets cold. You just wouldn't do that. You'd hop in your car, go a couple miles without any traffic, and use the free parking.
Heroin addicts aren't normally a problem in reasonable non-city areas. Yes, you could choose to live in the worst neighborhood, maybe renting for $200/month, but that isn't normal for a "software-engineering" person. More likely you'd be in a neighborhood where calling the cops about a suspicious person would get the cops there in a couple minutes, and/or you'd be in a place where burglars get shot at with full approval of the state legislature.
Mind you, that's all in the city where buses actually kinda suck. Where I'm from, subway runs 19 hours a day, and peak hour train interval are 50 seconds, up to 7 minutes at night. Many people still drive (it actually takes much longer at rush hour), well as I say, why stop the self-inflicted suffering, there are all kinds of kinky people :)
The way I see it, driving yourself is a menial job that makes about as much sense to do as pumping your own overflowed sewer with your own advanced plumbing gear. If you cannot pay someone else to do it (no plumbers or buses/ubers accessible), either you live really far in the mountains, or the place you live in is run by idiots.
Crime rates, except for the most benign property crime like car prowls and package theft, seem to be way higher in the LCOLs I looked at, ~4 years ago when we were deciding where to move to. I was actually surprised how much higher, although I don't remember the details. Anecdotally, someone I know lives in a LCOL in Texas and they got burglarized no problem in a gated burb that is way far out, you cannot get there in any way other than by car.
You must be very comfortable in crowds, without much concern for the fact that some other person could do something bad to you. Suburbia exists largely because other people disagree. These other people can not relax on a city bus.
Fixing your own sewer is something people do for privacy (strangers again, IN THE HOME), scheduling, and to take pride in doing something with real physical results. It's like cooking your own food, changing the oil in your car, walking your dog, washing your dog, teaching your kids to read, driving, and mowing your lawn. All these things can be paid for, but that takes variety out of life and reduces privacy.
Getting burglarized in Texas is pretty special. Somebody knew he wasn't home, or at least that he wasn't armed.
I shouldn't be walking for groceries. The HCOL/LCOL distinction sorts by family size, being both cause and effect. (you choose a place according to family size, and then the choice you made will influence your family size) I have 11 kids, so try to imagine hauling the groceries for 13 people.
Going by your price, it's $35.75 for us to take the bus.
For an average person though, preference for suburbs is usually just based on outdated preconceived notions and habit (scared on a city bus? buses in HCOL areas, esp. those going to major white collar employment areas e.g. Seattle to Redmond, have like 30% of the people on their laptops half the time; uncomfortable in crowds, in the US? most US cities have no crowds to speak of even in downtown core, and in any case most people are quite fine in a crowd at a football game or a concert).
Also, even with an extreme bias towards suburbs in the US ("the children!"), many people do prefer cities if you judge by the price per sqft.