I have phoned in to skip 1st segment, already had 2nd segment BP, phone agent plat line did it without any comment, gate agent flagged me down at red beep, I paid in 5 minutes after two minutes unsuccessful negotiations and boarded. No problem. No reprice. 150 Euro. KLM in Amstersam. Outstation might be a mess. This was once. Most of the times I paid nothing but also had a good reason or Irrops or something.

I think there is a lot of assumptions here. Fee plus reprice - not in my experience.