Why not wire transfer? Here bank transfers are very cheap (free for most people unless you do a lot) and usually take a few hours at most (at some banks are instant).
If someone requests anything else as payment for rent you can be fairly sure they try to evade taxes on it as wire transfer is both the most convenient, cheapest and the safest way to pay.
Wire transfers in the US are expensive for most checking accounts. In the $20-40 range per payment. Also people don't usually carry around their account numbers for receiving payments.
Are you talking wire transfers or ACH payments? ACH is typically a much slower method of transferring money (1-5 business days) though it is generally free to do so. ACH also carries all of the risks associated with checks save the risk of losing a piece of paper before you can deposit it.
Wire transfers can happen almost immediately but typically cost $20-40 for one, or sometimes both, parties involved.
Most banks allow you to transfer between accounts at the same bank for free, and faster than ACH transfers because they can settle it quickly when its internal.
Fair enough, but venmo/google/apple pay is even more convenient than wire transfers and they're not into those either. Checks/Cheques are just a cultural norm in America.