How is it more uncomfortable to have unambigiously rejected someone vs letting someone down gently?

The awkwardness is in the person making the approach. And that is done already, if a rejection is necessary.

If anything at all, the rejection leading to a second approach, as it wasn't a clear enough rejection, that is what leads to more awkwardness.

The person infatuated and being rejected knows what she or he can expect and it helps them being more professional.
Yeah, you probably can't be colleagues AND friends, and yeah, it will be embarrasing for the person doing the appraoch if other's know about the infatuation and the rejection, but that's something different.

I don't see how leaving a doubt in the mind of the infatuated person is helping it be less awkward.