It really wasn't just MH. I think I've thrown out the numbers before, and I don't really want to get all the numbers together now again to illustrate the point (unless there's a huge interest in the subject, then I could do it tomorrow), but basically while MHP remains the biggest success on the PSP in Japan, the franchise started booming on the PSP along with several other releases, and it can be seen that developers and publishers were already making more and more PS2 level titles for PSP during the 2005-2006 period, which coincides with when MHP was first released and started to gain popularity. It was a combined process and the other games also helped MHP, because the series didn't become super huge over night.
The general flow of more constant software helped the PSP sell, and as more people got the system they gravitated around MHP as a series. It's not like they released MHP and suddenly everyone bought a PSP on day one because they had been waiting for this game. The MH series wasn't even that popular on the PS2 in comparison. The explosion of MHP fever really only started in 2007-2008, by which time the PSP already had quite a number of ~200k+ titles.
The combination of MHP2's explosion along with having number series which were doing over 200k at the time with multiple releases over the years (Tales, Gundam, MGS) definitely triggered a much larger wave of developers to move in after that, as evidenced by the increase in software offerings each year moving forward from 2007. By then, it is as you said, the natural choice, but it didn't get there entirely on MHP alone.