Okay. Yes, I was surprised by the lack of error messages. I was also surprised that similar discs seemed to work, even similar discs from the same company (something I probably should have mentioned, my bad). Mega Man X4 and Darkstalkers 3 worked just fine, whereas Mega Man 8 and Darkstalkers 1 did not.
Age of disc itself didn't seem to make a difference either, since the most recent disc that wouldn't read was King of Fighters '99, whereas Fatal Fury: Wild Ambition, also made by SNK and released earlier, ripped just fine. Then again, I'm looking at the disc now, and it seems that they might have released Playstation version through different distribution channels. Hadn't realized that before.
Anyway, regarding the "bad sectors" argument, I did wonder about that since I do recall something about certain companies using that to discourage unhealthy activities, though I thought something about the disc coating was supposed to make that unnecessary (or that it only affected more direct burning methods, etc, perhaps that's a silly thought), or that they didn't use that until PS2 era and afterward. It's been a while and I guess I'm a little out of touch.
Then again, maybe the disc(s) really are just holding up enough that they'll still play just fine on the hardware but won't rip. Just that I can see it isn't a simple program issue, and I was sure that it couldn't entirely be a hardware issue, though I did consider that. Thanks for the advice, either way. I'll see what I can do.