It most certainly is not. In nearly 20 years of owning a home, our property tax has never been escrowed. I don't want to give the bank a free loan for that money, even if it only earns me $3.28 in interest.
And no, renting a home doesn't mean you are paying someone else's payments. (And even if you are, assuming by "payments" you means P+I and property taxes, that doesn't cover maintenance, insurance, and other costs, plus vacanacy time and probably a PM, if we are talking about making it into an rental property). Where I live (a VHCOLA area, admitedly), a $1m home probably rents for about $4000. A $1m mortgage has a payment of about $4300 (30 year, 3.25%). so already, renting is better. And that's before any property taxes, insurance, maintenance, or anything else. That's JUST the mortgage.
And let's not forget that while yes, rent is money flushed, so too is interest. And for the first few years, nearly all of that payment is interest, so you are flushing a lot of cash there. And since your monthly expenses are more, you are flushing property taxes, insurance, etc. While the renter is investing his $300mo difference, plus ~$300/mo he isn't paying in property taxes (probably a low to very low estimate!) and another $400 he isn't paying toward maintenance. So he's got $1000 a month going into VTSAX, while the person who buys that property has paid down about $20,000. Not a huge difference (though I didn't address HOA if applicable, and insurance differences), but our renter comes out ahead. BUT, we are talking about investment properties. So we need to add in $2000/yr for a very optimistic vacancy (2 week turnaround) and $4800 for a property manager.
So yeah, buying that house ends up costing a lot more than renting it. And no, those aren't made up numbers. That's my neighborhood. In San Diego, the house we own (because we were suckers who bought into the "owning rental properties is the path to wealth!" mantra and didn't sell when we moved) rents for about $3000/mo and would sell for about $600,000-625,000 (or a $2600-2700 mortgage payment, P+I only) and probably close to $600/mo in property taxes (we pay nearly that and prop 13 keeps our taxes lower than they would be for a new buyer, so again, that's a low estimate). So before a PM's fees, insurance, HOA, and maintenance, for a new investor, the renter has $1000 more in his pocket each month than his landlord.
And I don't think most people can DIY a new roof or refrigerator. And if they have the kind of job that moves them away from the home they own, they can't DIY the running toilet or the vanity replacement or anything at all.