I don't disagree that they own it, but I disagree that it's a bad movie. I actually found the movie largely enjoyable even without its real world context, but I acknowledge that this is a matter of personal taste.

The Wachowskis not being involved wouldn't have affected the movie's commercial success. There are plenty of examples of "franchises" being carried on by different directors even in directions the original director never intended and to still be successful.

What the Wachowskis did was take a story that had nothing left to tell and then make a movie about the experience of having to keep adding to that story, drive home the point of the original story and provide an ending to the story that is impossible to write around without discarding the source material and starting over (not that that stopped e.g. Star Wars Rise of Skywalker from doing pretty much this with The Last Jedi).

The Matrix is intrinsically anti-capitalist, anti-authoritarian and queer. But much of its fanbase likes it entirely for cosmetic reasons (cool slomo fights and explosions and sunglasses). WB would have been entirely happy to cater to that crowd and would likely have gotten away with it. Instead the movie ended up amplifying those themes and alienating anyone who just wanted another film with cool slomo fights and explosions and sunglasses. And IMO they did it in an interesting way nevertheless.