I've had a few assembly companies ask for ODB++ files, so I'm not surprised. It's supported by many tools these days. (I don't know about the future yet...)
The benefit is that it certainly saves a lot of time for them, but not just that. Also a lot of potential human errors, compared to providing them with additional information in a non-standard form. Of course if you absolutely can't generate ODB++ files, then they should accept that. I've found that many these days ask for ODB++ by default (for the above reasons), but will of course deal with information in other forms if required. Just tell them your EDA doesn't generate ODB++. End of the story, as not all EDA packages do. EDA I've used that do support ODB++ export: Altium Designer, Zuken Cadstar. KiCad doesn't support that AFAIK (at least as of now.)
There is no way to "convert" Gerber to ODB++ as standard Gerber doesn't contain the equivalent information, not even with Gerber X2. I don't know anything much yet about X3, but if anything, we're talking about a few years ahead, not right now. For instance, ODB++ include pick-and-place data that can be automatically imported for pick-and-place machines.
As said above, assembly companies should accept projects with no ODB++. I even bet that's still the majority of projects most of them deal with. Again they just ask for that routinely because it helps them significantly, but they shouldn't reject your project if you don't have that. If they ever do (or charge you significant extra), then go look elsewhere. What you could do, though, is ask them what's their prefered format for pick-and-place (component location) files, and try and generate that to make things easier. Usually some kind of CSV format is fine as it's easy to import/process in many software tools. They may have a prefered column order for the data - you can ask. In any case, they'll have a technician or engineer to prepare files for the machines, so that should not be a showstopper.