Yeah, and then you find out that that constant was also used in another piece of code as number of minutes, so you've just changed another timeout in the system from 10 minutes to 10 hours.
Yes, of course that constant should never have been a naked integer in the first place, but we live in an imperfect world. One thing I like about Go's standard library is that almost everything takes time.Duration instead of a plain integer that's then interpreted to be milliseconds (or micro/nanoseconds in the most unexpected place, gotcha, developer, you should've read the docs!)
If the bug is "I thought we were supposed to have a 10 minute timeout and we accidentally set the timeout to 10 seconds" it's pretty screamingly obvious that if you change the time from "10" to "600" the problem is now solved and you haven't broken anything else.
Religiously applying this rule of thumb as you describe causes ALL sorts of problems including the problem of people writing tests for the above kind of behavior. That test will fail when it's changed from 600 to 1800 deliberately and that will create a pointless waste of time for everybody.