Is there a[n] irrefutable requirement to have a log function without explicit
level?

As I understand, it's a defensive feature. There are things one wants in the log unconditionally, like OS version and program version. They can be logged at fatal level, but that's a workaround and looks confusing, and still can be filtered.

Believe that's what the 'off' level is for, though it is confusingly named (off as in no filtering, not no logging). Maybe better called 'always'?

I contend that having bare log methods without a specified level is a mis-feature. They may be useful as a shortcut when the desired level is unknown/irrelevant, but I don't believe what they add is worth the bother.