Sadly yeah, the problem with backwards compatibility is hardware fusion between the newest gen and old gen, which unfortunately would cost more (according to them). So they had to use software emulation to run them, which at times can suck or just not compatible with a certain game that ran on hardware.
There are a few PS2 and PS3 games I wanted to play or never got to finish. It seems like a weird journey getting PS2 compatibility or PS3. Think they could just improve on software to run it or something, but that sounds also tough if you get past games running on 40-50 fps.
Yeah DOA ran on hardware so it makes sense why it wouldn't do so well.