The same way you can take say you’re earning 10% on your down payment if you put it into the market, even though you have to reduce your investment by $X per month every month for rent.
The simplifying assumption is that you’re paying your rent out of funds that aren’t your investment funds. The parallel simplifying assumption for the ownership side of the ledger is that you’re paying your mortgage out of funds that aren’t your investment funds as well.
You’re absolutely right that the home calculation does not accurately reflect the entire impact on your finances, because (of course) you still have to pay the mortgage. But similarly, the rent calculation doesn’t accurately reflect the entire impact on your finances, because (of course) you still have to pay the rent.