Sorry for English and my rude action,I just notice this topic have something have little bit lose, the follows PSP software are support media install and didn't listed.
2008
CLANNAD (Key)
planetarian ~ちいさなほしのゆめ~ (Key)
智代アフター~It’s a Wonderful Life~CS Edition(Key)
神曲奏界ポリフォニカ 0~4話フルパック (ocelot)
ハートの国のアリス (QuinRose)
学園ヘヴン BOY'S LOVE SCRAMBLE! (Spray)
※ List of upper games are converted by "Phorotype"(プロトタイプ_(企業))
Also, I found a noticeable thing about the term of "media install"(メディアインストール), Look at "機動戦士ガンダム ガンダムvsガンダムNEXTPLUS"'s manual page 25, that have a little words declared "media install" is "Capcom" (カプコン) registered trademark.