It's not $134k to break even, it's is that $134k less than $[YOUR RENT OVER 7 YEARS]. Unless your suggestion is we should all go homeless.
But your landlord also has to pay property/school taxes. Your landlord has to pay HOA fees. And landlord fees, business taxes, administration fees, accountancy fees, or whatever delights the US tax systems have conjured compared to the UK one.
And they have to make money. Otherwise they'd just sell the house and put the money in a tracker fund. So they have to make 5% per year on $250k. Which comes out at...
$1250. Oh, how odd! It's the same as the 4% mortgage payment (smart readers will notice that's today's mortgage payment, not the low mortgage rates over the last 10 years!). Or they put 20% down on the house and pay a mortgage. For a higher amount than a home owner. With no tax breaks.
So they have a base price, $1250 + taxes + HOA, etc. ANything less than that and they should just stop being a landlord. A quick google brings this up about the US rental market:
The amount of rent you charge your tenants should be a percentage of your home's market value. Typically, the rents that landlords charge fall between 0.8% and 1.1% of the home's value. For example, for a home valued at $250,000, a landlord could charge between $2,000 and $2,750 each month
So the advice for minimum rent on a $250k house in the US is $2000, minimum.
7 * 12 * 2000 = 168,000.
So the question is, do you want to spend a minimum of $168,000 on rent. Maybe up to $231,000. That's what you will lose on rent. There's no "break even", you don't benefit from house price rises. That's dead money you're never going to see it again.
Or do you want to spend $134k on home ownership? And have $35k in equity (which you conveniently left out of your calculation). Probably much more equity than that because of inflation and house price rises, unless you bought when houses were at a peak.
What you've got wrong is that the "cost" of buying vs renting is actually the one-off fees you pay each time you buy a house. The lawyers fees, the mortgage arrangement fees, the legal searches, etc. The cost of selling your home (the estate agent fee, realtor in America I guess). In the UK we have a tax too, stamp duty, when you by a home.
And if you move in 2 years you have to pay all that again.
That's why it sometimes make sense to rent vs buying.
But long-term, buying is always better, because landlords have to make money and have the same costs as a home owner. It's basic economics.
And over 7 years? No contest. Buy.