One of the many reasons I haven't followed wrestling on a consistent basis and haven't considered myself a fan for some time is my belief that in WWE, the titles don't really mean much and haven't since the whole brand extension mess. While there have been glimmers of hope sprinkled throughout the last 10 years or so, ever since they began flooding the company with titles and establishing two heavyweight WWE championships (not to mention a US and Intercontinental title), the company still hasn't quite figured out how to make these stupid things seem even remotely important. Having two top titles is like having a Best Picture and Best Movie award at the Oscars.
To the best of your knowledge, which of these is true: A) Vince and company know full well these belts don't mean what they used to and simply don't care, or B) They aren't aware a lot of people feel the same way I do and truly feel fans care about these ill-defined and diluted championships. And now that I think of it, if the former is true, why do they not care? Why do they still feel such a need to keep around two world/WWE titles when they isn't even a brand split anymore — not that they did a bang up job with them when they did have a split in the first place?

They don't care.  Titles are still around basically because titles have always been around and it's considered a necessary part of the show, but the company doesn't care and neither do the fans at this point.  You'll get house shows with 4 or 5 titles being defended and it makes no difference to the attendance whatsoever.  I hate to keep beating a dead horse, but it's mostly because of what Vince Russo did to them during his run, as they became literal props on a TV show.  They keep them now because they've always been around and you never know when they might need a quick title change to pop a rating.  That's really all there is to it now.