You are not accounting for property tax which can significantly affect the payment. If property values rise, which they always do it will increase the payment. Making the saving from this moronic plan meaningless.

No it’s with 5.5% interest and a measly 5% down payment.

good luck finding a 350,000 home

This is going to vary wildly by region. There's tons of large cities where the going rate for homes is around 300k and there's notable large cities where you're lucky to find any property for under a million.

Depending on the market you might simply need to lower your standards if you're filtering by homes built too recently or homes with a ton of square footage or a high number of bedrooms/bathrooms. Or you might be in a truly fucked market where your best bet is to get creative and either buy a home with friends and/or family or even buy a home with a family member or friend helping with the intial mortgage and then rent out some space or find some other hustle with the property (I've heard of folks buying homes & property in the country and turning it into a wedding venue for example. Or renting it out for film shoots or AirBnB or whatever else happens to work where you live. I know a guy who built an ADU just to rent out on AirBnB as a side stream of income)

Even the homes that are 40 years old in my area

That's...extremely new even by American standards. I say this sitting in a home which was built while the ottoman empire still existed. Yeah there's quirks and it would be nice if the home was built to more modern standards, but it's nothing that a bit of creativity, ingenuity and maybe a contractor or two when you can afford them can't sort out. Plus the equity I've gained in just a few years makes it a damn good choice that I bought when I did and didn't wait until I could afford to buy the perfect house

So getting a home at $260,000 that you got would be a dream.

Hey, the house across the street from me is listed at that right now. It's got a pool and some nice updates, decent amount of bedrooms and bathrooms. Cute place. I live in a pretty small town so you might not like that, especially since job availability can be a struggle here even during good job markets if you're in a white collar role. On the other hand if you're willing to change careers entirely it's pretty affordable. Guy who's selling it works for a landscaping company and mows lawns on the side for several folks in the neighborhood. Or I'm thinking I'll go be a school bus driving as a backup if things go south with my employment status for example. See above about either lowering your standards to what you can afford or getting creative if you're in a more fucked market.

Ultimately life in this world is all about finding the best way to enjoy the opportunities available to you. If you've got a career you love living somewhere you love maybe it's worth renting for an extra decade or two until you can finally afford to buy. Or maybe you aren't fully in love with your career and/or where you live so relocating or a creative change to your finances might make sense.

You can still find sub 50k homes, but you will have to temper your expectations for the area and condition. Can't be afraid to learn a few renovation tricks and get your hands dirty!