The missing IWC stamp would definitely make me want to document the watch carefully, even though the Cal. 58 identification looks reassuring. Since you already have both the movement and case serial numbers, I’d keep those recorded together with clear photos of the movement, case, dial, and inside of the case.
It would also be interesting to compare the movement and case numbers against the known IWC production records to see whether their period and configuration are consistent. If the watch is going to be serviced, I’d avoid polishing or replacing anything until its originality has been properly assessed. With a vintage piece like this, preserving the existing condition can be just as important as getting it running perfectly.
If anyone here has access to IWC Cal. 58 serial-number records, it would be interesting to know what production period movement 176848 falls into and whether the case number 214906 is consistent with it.