My hypothesis is that the P-series frame and/or 3PH are too big to accommodate the "quick attach" LS BH and its subframe, and also that the subframe assembly would negatively impede ground clearance to the extent that it is not practical for use on that tractor. Additionally, the OEM who provides LS with BHs may not make one for that size tractor, and it just isn't worth the extra costs involved to get another vendor and engineer one for the P-series based on likely low demand. Albeit, if they did, I bet that it would be a BEAST and match the giant size and capacity of the P-series!
Still trying to identify who the OEM is for my LS XU5065CPS BH -- based on Kioti's DK/DS-series BH performance specs, I believe they may be the same unit with different paint color. When everything gets here I'll be sure to compare pics more closely and follow-up to confirm if the Kioti and LS BHs are the same. Yesterday I was reading universally positive reviews of the Woods BHs here on TBN (most had Kioti tractors), so aftermarket BHs could be a "better" option depending on the kind of BH performance you desire. From what I've read, however, I'd only go with an aftermarket BH that mounts via subframe. The P-series huge 3PH capacity and size may be the exception, but I've read/heard enough horror stories about 3PH-mounted BHs that they didn't even make the consideration list.
p.s. Great price!! I'd be jealous if the P7010 wasn't just too big for all of my goldilocks needs...