Is it OK to run it this way?

Nope

If it's running stably in that position you're not hurting anything. For
some reason the mixture with the choke off is too lean and leaving it
partly on corrects that. The engine is then getting what it needs.

Is a repair necessary?

Yep

It *should* be repaired but it's not like it's hurting itself if it's
running smoothly.

Of the possible causes previously given it won't be a dirty air cleaner as
that would have the same effect as the choke, richening the mixture. Fuel
filter....maybe but I wouldn't bet money on it. Carb adjustment...well
that doesn't change by itself but readjusting it could fix things. (Back
off the main carb adjustment screw maybe a turn and see if it then runs
sans choke.)

I would guess the problem is caused by dirt in the carb's fuel passages.
Repair would require disassembly with some tiny parts to deal with and you
still might never find anything specific but a general cleaning and
reassembly might correct that. But that might not be something you want to
get into. For now I would just try readjusting.