In my area, the average is right around $450k, so I think we're pretty representative of the rest of the US. I did a quick search, and I saw a dozen or so listings for townhouse around $300-350k. If we look at the top end, with a 20% down payment ($70k), the mortgage+HOA is ~$2500/month. If we look at the bottom end, it's ~$2300. I even see one as low as $2k/month. Note, this doesn't include utilities or maintenance. So for an average household income of $6275, we're looking at 30-37% of your income for the mortgage + HOA.

Rent for a similar place (2-3 bed, 2 bath) is $1500-2000. So it is currently cheaper to rent in terms of cash flow, but buying keeps your payment constant (inflation will be on your side) and builds equity, so longer term it should still be cheaper to own vs rent.

left with $300/month

Are you assuming a massive $800/month transportation budget or something?

Let's assume $6275/month income, here's a budget that I think makes sense:

• mortgage + HOA - $2500/month (could save $200 or more buying a cheaper place)
• food - assuming 4 person household with young kids (two under 5, which should be the target for these houses) - ~$900 (if you don't have kids, it's ~$550); this is the low cost food plan, not the "thrifty" food plan
• transportation - ~$700/month; insurance ($50-100 in my area for two cars), gas ($100-150), maintenance/repairs (~$50/month), yearly registration ($100-150 in my area, so <$15/month); purchase price (assuming buying used and keeping for 10 years, a 2017 Corolla is ~$17k and a 2007 is ~$5k, so $1.2k/year or $100/month; add taxes and fees and assume ~$150/month on the high side)
• utilities - ~$300/month; we spend a little more, but our house is larger than the ones i referenced (2400sq ft)
• taxes without any retirement savings - ~$8000/year, or ~$670/month (my state is ~5%, federal is ~11% at this income, so 16% of $75k)

So, the major expenses come out to ~$5100/month. Add in another $500 or so for other stuff, and $5600 is a decent spending estimate. That leaves $600-700/month for savings, or 10-11%. Typical retirement savings goal is 10-15%, and that could be met by trimming some of these expenses by $200-250/monthn (a lot of that is taxes if going for pretax investments).

So yes, mortgage rates and property values certainly make things difficult, but I hope I've showed that it's not as hopeless and many people assume. I think the average household could own a house and still save 10-15% of their pretax income. They'd need to drive older cars, but nothing unreasonable (5-15 years old; both of my cars are 15+ years old and have minimal maintenance costs).

Unfortunately, the average person seems to suck at budgeting, which is why I say it's more often a budgeting problem instead of an income problem. The important thing is to establish good budgeting habits early, and then the focus should be on increasing income. Ideally, as your income rises, your spending doesn't rise as quickly, so you end up with more cash flow as you get to the point where you want to invest in a house.