Yes I believe it's a hassle to get passengers from the P lounge to landside -- I had to do it as I mis-connected and they had me wait in the lounge while they sorted out the flight for the next day and the hotel voucher (while they force-fed me foie gras
). Then someone escorted me to arrivals, but it was kind of a long, roundabout walk and I had to clear immigration (I think they had cleared me out of Schengen on arrival to the P lounge -- which I suppose is legally outside of Schengen? -- and so I had to be cleared back into the zone to get to the hotel.) It certainly makes sense that they wouldn't want to do this on a regular basis.
(And FWIW, also CX only allows F lounge access after an inbound in F if the onward segment in J is same-day.)
I think the only real question was one of policy - whether AF would recognize the same-day connection on a separate ticket and provide P lounge access based on the inbound P ticket. (And I defer on that).