Earlier quoted context omitted.
They certainly do. In Chatty: https://source.puri.sm/Librem5/chatty/-/merge_requests/786 . Some carriers even charge for the service (!!): https://source.puri.sm/Librem5/chatty/-/issues/434 MMS has delivery reports too (I implimented support for it myself for mainline Linux Phones). It even has read reports, but no carrier seems to honor using it (which is why I didn't bother to impliment it). I'm not sure if Android…
There is an option to enable delivery receipts on Android (Google and Samsung). I believe it is disabled by default.
I'm not sure if SMS supports read reciepts, but I didn't think so. The MMS standard allows for read receipts ("MAY" not "SHALL"), I was unable to get it working, and I suspect it's due to no carrier support.
I was unable to get read receipts working at all, and I suspect it's because the carrier doesn't impliment it.