That's just how it was designed, & how it was intended to be used.
Dolby C is supposed to emphasize the highs & mid-highs on recording, and de-emphasize the highs & mid-highs an equal amount during playback, thereby diminishing tape hiss in the process. That's by the book, anyway.
I'll agree, that any Dolby NR (A, B, C) does a less than stellar job of eliminating hiss while leaving the original audio unadulterated, & that's why I prefer Tascam/dbx, but that's another post.
I'll have to admit, that on my common household cassette decks, I'll typically record WITH Dolby C (on) and playback WITHOUT it (off), but that's just a personal preference, and is not "by the book", at all. In my experience, with Dolby C engaged on cassette recording AND playback, it does seem to sap a lot of the highs out of the playback,... more than would warrant for nominal tape hiss reduction.
Our friend has an E-16 w/Dolby C, and that's not too shabby for starters, but I'd still recommend the Dolby C is left ON during recording and playback. That's by the book.
However, as with anything like this, Dolby C NR is highly dependent on proper calibration of internal levels, for optimum performance,... and that's where a lot of real-world recorders fall short. Typical home recording analog setups are almost never calibrated, in their entire service life. Why that is, is probably more of a socioligical question than a technical question.
BTW, any other record/reproduce system and NR system will also perform to it's optimum when the internal record/reproduce levels are calbrated to spec. However, that's hardly ever done,... unless you're a hardcore DIY'er like me, or if you have a pro service technician calibrate the recorder for you.
I'm heavily weighted in Tascam/Analog with dbx, but I'll admit to having a few Fostex/Analog recorders with Dolby C, plus a few token analog/digital hybrid porta-format recorders.
Rokket, I didn't catch what your main recorder is at this time? Thanx.
=============
Bottom line: I'd advise the E-16 user to record/playback with Dolby C engaged. Thx.
=============