Probably a minority opinion but I'm actually not a fan of how this rule is structured (I believe it's the same for NCAA as well as NHFS.) I get that while K can advance a ball that does not cross the LOS, IMO a valid FC signal should buy him at least the same protection as an invalid FC signal, where he is granted the opportunity to catch the ball, simply from a safety perspective - he's made it clear that he's given up the right to advance the ball, and as written this is a prime opportunity for R to crater him, while he’s in a vulnerable position, with no consequences. If he doesn’t give a signal, fire away, level him, whatever, because he didn’t indicate he was trading advancing the ball for protection. In almost all cases, I would wager that if K is signaling for FC, they are not expecting to get popped in the mouth unexpectedly.
If K drops the ball, great, it’s a live ball, R can pick it up and advance, and they’ll always have that spot as illegal/first touching spot. If it’s caught, R gets the ball in a what is likely very advantageous field position, because the ball is immediately dead.
And OP - this is more likely to occur than you think! I had a play this past season where K punted, and the combination of a stiff wind and a poor kick caused the ball to land -1 yards behind the LOS. The ball bounced, and K recovered in on the fly, then tossed the ball forward to his sideline, because he thought it was a dead ball, and the R whistled it dead when he possessed it. So we had a weird confluence of a IFP, with IW. After a quick huddle (and a peek at the scoreboard, K was already down by 30 or so, late in 3rd quarter with no hope of even remotely getting close), we just gave the ball to R at the spot of the recovery. He just as easily could have given a FC signal and tried to catch it. IN the end, no one blinked an eye at how we handled it due to time/score (if anyone even knew, which was doubtful) and as Ralph would say, the band played on...