I'm not really seeing that happen for a couple of reasons.
First, physical sets like in the backlot are way more practical for most productions. The Volume seems to do really well for things like Sci-Fi and Fantasy where you can't exactly go out and film on location, but you would still need digital artists to create those environments to then put up on the screens. For something like a city scene or a small, suburban community, it would be so much easier to just use the backlot sets that already exist. Not to mention that, while larger productions may use things like The Volume, it may not be in the budget for smaller or mid-tier productions to utilize something like that, whereas using the backlot for filming would be much more economical. Plus, and you can pretty clearly see this in the latest Antman film, that sort of filming can create a disconnect between the actors and the environments that their characters are supposed to be in.
The other big reason I don't see them giving up backlot space for attractions is that it's really impractical from a theme park perspective. Even setting aside the fact that the Studio Tour is a huge draw to the park which would have a lot of its value reduced by the reduction or elimination of backlot sets, the backlot sets are just pretty far away from the rest of the park. It's a quarter mile to get from the lower lot to the metro sets, and that's assuming that they plop down the theme park expansion as close to the park as possible. What seems more likely (and what they're already doing/have done to some extent), is that they might trim away at the edges of the backlot to have more room for additional soundstages, which them allows them to remove soundstages closer to the park itself.