Don't know for sure, but I would guess there are a lot of reserve/youth players sent out to BSP/BSS/BSN sides. You may be allowed 8/11 to be loanees, but that's over the course of the season and I was under the impression there was a limit on the number of long-term loanees you could have (i.e. 4 long and 4 short).
As for the situation being 'incredible' that people will go to BS teams on loan but not League 2 on permanent deals...I don't think it's that incredible at all. A loan is temporary, so player X knows he will get experience, probably not find it that hard, and will go back to a better club. By the same token, he also knows that by transferring to League 2, he will probably never see the
Prem or Championship again, unless he gets there with a League 2 team that gets promoted to that level (eventually).
Looking at the situation IRL, foreign competition, high (unrealistically so) fees and lack of experience at a certain level usually means the only mobility for players these days is downward. If Stuart Pearce and Chris Waddle were starting out today, with Wealdstone and Tow Law Town, they'd get nowhere near the league, let alone the top flight and England squad.
For this reason, both IRL and in FM, players will be happy to go down divisions on loan, but not permanently.