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.
Fair enough, but I'm not entirely convinced you know. Here's the reasons:
At launch (2004), the best selling game on PSP was Hot Shot Golf, which sold 400k. Second best selling game was Dynasty Warriors with 290k and Ridge Racers with 270k. Nothing very significant, since there are launch figures. Let's move to the next year.
2005: best selling game was Monster Hunter Portable with 670k. Second best selling game was Nou Ryoku Trainer Portable (Sega) with 300k. Third was.... Hot Shot Golf the Best with 260k. WSWE9 follows at 240k and Tales of Eternia at 190k. Clearly Monster Hunter already makes the part of the lion here. Nou Ryoku trainer sold a lot following Brain Training on DS and Tales of was sure not a significant gap filler as you states imo. Let's move anyway to 2006.
2006: Metal Gear Solid Portable Ops 350k. Monster Hunter Portable THE BEST......290k! Nice showing of MGS
O, but the real surprise here, again, is Monster Hunter: selling almost the half of the first release! SD Gundam then 290k and Tales of the World 210k. Not really a nice performance. Again, the lion here remains monster hunter, since it's the only performance way better than foresaw.
2007: Monster Hunter Portable 2nd 1'700'000. Wow. This is something crazy. Crisis Core FF VII 800k. MGS: portable ops Plus 350k.
Bottom line is that PSP was revitalized essentially by Monster Hunter. About the other franchises, the only thing we can say is that maybe they prevented the handheld to totally die, but I wouldn't affirm they contribute to PSP's success. Personally at that time, the additional functions of PSP (video, mp3 player, etc) were considered the main reason people were "buying the system without buying games". No. Monster Hunter did it entirely and these numbers show that. The differences are too huge and one can affirm that already there was something different even when the first Monster Hunter launched and persisted with the release the best. It was the right game for the right platform with the right audience. Crazy hype and well orchestrated ads made the rest. But the other games....they sold in line with expectations or even less than foresaw and weren't that significant.
