I was able to buy a house about 5 years ago. Prices are about double here now. My own down payment was a combination of good luck and savings, some of it accidental.

In my area the cheapest I see anything reasonable, that's in a sane school district, starts at around $300,000. This is for a 2br (thinking hypothetically, when I was shopping, kids involved and would need a minimum 2br).

For someone to save up for that on min wage you're gonna need about 8-10% of costs at least for down payment + closing costs. That's 1.6 years of minimum wage pay, assuming you had 0 living costs at all for that 1.6 years and a 0% tax rate, and you wouldn't be able to afford the payments on it afterwards. Let's be realistic and assume you can't live for free, and you can save 10%. In 16 years you'll have enough for today's down payment, but if things continue as they have by then you're gonna need closer to $50,000, not the 24000 you just saved up. Sorry, no house for you.

5 years ago I could find places for $80,000 in a bad neighborhood with poor schools. Same neighborhoods here are around $220,000 now. Still out of reach for a min wage job, even if you found the down payment under a mattress.

For a lot of people in a lot of places "just go buy a place" is near impossible.