There are cron implementations that handle the "turned off at night" problem. anacron is one of them.
Even running updatedb (except the initial run) and then running locate might be faster than running a recursive grep from the root directory. Definitely if you run that grep more than once.
Re:Linux Productivity Tools (2019) [pdf]
by everybodyknows on Tuesday May 19, 2020 @10:55AM
(#23235535)
>you run updatedb manually all the time and weep because that's not something instant, at all.
No, not instant, YMMV. On my mid-range laptop with SATA SSD:
$ time sudo updatedb
real 0m0.501s
user 0m0.247s
sys 0m0.218s
All in all, the idea is good, but I'm almost sure there are better implementations (even Windows has tools like 'Everything' which use a database but which gets continuously updated).