By that logic one could say that Sony should give me the Last of US remastered because I already own the PS3 version, obviously we can agree that that is unreasonable because the remaster had some work done to it to enhance it, but why can't the same logic be applied to these PS2 games, it's clear some work went into making the PS2 emulator, not only to enhance resolution but to also add trophy support and make sure it performs well, which means some sort of QA for each game. So although these PS2 game on PS4 was significantly cheaper to release than porting it to PS4, it still cost time and money. We don't even know if it's a full emulator or one that has to be customized per game.

Another thing to consider is the complexity and task of attempting a full scale emulator that people want, the PS2 has around 4000 games in it's library, even the best PS2 emulator out their,  PCSX2, still has graphical glitches and other issues which people report on their forums, it was even worse when the emulator was starting out, I hardly think Sony would release such a glitchy mess just to claim they have backwards compatibility even if it could play 50% just fine, people would not be impressed and would be rather annoyed if the emulator was that hit and miss, it's why I think they've taken the more controlled method they have, choose games people may like and get the emulator up to scratch and then release it. Over time and through customer feeback they could definitely build a very capable PS2 emulator in a quick time frame, so their could be a possibility one day of an actual disc based emulator, but they'd probably sell the emulator for maybe $30-$60 to get some return on investment.

On the other hand, if they could just copy paste their old PS3 emulator across to PS4, that would cost them almost nothing, in this case yeah of course they would of given disc based emulation, they probably wouldn't have bothered with trophies, just simple cost effective ISO dumps to the Store, no harm no foul for those playing using their discs, great public relations to combat Microsoft backwards compatibility....but that's clearly not the case, it looks like they may have to have re-writtent the emulator from scratch to work on the PS4 different architecture, they would of also been able to estimate the cost of building and emulator from scratch based on how much money and time they spent building one on the PS3, so maybe the way things have worked out were the only option to make PS2 games on PS4 a thing...that's my educated guess at least.