Since you mentioned finishing tape, I have to say I've been using clear Scotch tape as finishing tape, which can be laid down wrinkle-free if one compresses the tape onto the bar wrap as the tape is being stretched lightly as it is coming into contact with the wrap. I put down two or three complete turns, and it's doesn't slide itself loose over time like electrical tape usually does.
With the clear tape in place and holding the wrap securely, the logo tape can then be applied for a finishing touch, using a small spot of wet contact cement on the adhesive side of the last inch of tape, then compressing the last inch of tape into place using a sliding action with a balled rag, which slowly squeegee's the wet glue out into an almost immediately-dry super-thin layer that will never let go.

As for friction tape, I don't care for it's gummy texture, it's not padded, is unattractive imo and doesn't stretch well. It is just the thing for your hockey stick blade though.

This week I put 11 hours into refurbing this Schwinn Tempo that had spent a good few years outside, got it at Goodwill for 44.95, and was lucky to un-stick the deeply-inserted seatpost with less-than-expected torque from my 18" adj wrench.

I removed the crumbly Benotto tape in preparation for installing this longer 10cm stem.
I then took used, discarded padded tape from the shop's trash that I then ran through the washing machine with my clothes, and used the above methods for finishing the wrapped tape. It will fail from wear before the finishing strip ever comes loose!