That should actually work. I am currently on ESPHome version 2023.3.2 and can confirm that setting a longer update interval for the template text sensor works.
The other thing to remember is (at least that’s my understanding) that even if the last restart time is sent every minute, because the value has not changed this should not be registered as an update in HA and thus not write an entry into the database.
Compare that with an actual uptime sensor that changes its value every single time, this would result in a state change and a new entry in the database.