You've hit on another common complaint from the HD partner. Since it takes two to tango, the LD partner always ends up calling the shots. Even if you can convince them, it's still their decision whether or not to ML.
I can't tell you what to do or if it's worth the effort in your particular case, but it's worth it in mine. If you've read my posts you know that I've been married for over 28 years, had absolutely NO sex for the first 12, and have had next to none since then. It's very hard and I have loads of problems. Many times I've thought that it's not worth it and that I should just move on to someone who appreciates me and with whom I'm more sexually compatible. But in the end, I always come to see that my W has many sterling qualities, that apart from sex we’re really very compatible, and that the good outweighs the bad. But that’s a decision only you can make.
If there are children involved, then I would VERY strongly argue for staying and putting in whatever effort it takes. Do what you can and make the best of it. If there are no kids it becomes a little easier – but only a little. Only you know if the good outweighs the bad. Only you know how much or how little you value the R. I personally seem to swing between fairly accepting of the sexless sitch and miserably unhappy with it. My only recommendation to you is to make sure that any decision you make isn’t made in the depths of one of the downswings.