OP: This is the problem. No one wants to separate because both love each other. Both love the company of each other and the life they have together. Both prefer life together than not together.
But one yearns to have a physical relationship. The other doesn't want one.
It's a catch22. Choose to stay together because life is better together than not so therefore gave to live with a never to be resolved yearning and lacking of a physical relationship
But life is not better together than not really is it? It just seems that way.
Unless you count being tortured - constantly climbing the walls, not even being able to watch a sex scene in a TV clip or movie without feeling a regretful pang, sleeping next to an object of desire but never being able to touch sexually. Allowed to touch, but not touch too much. How do you think a hug or holding hands feels knowing there is underlying rejection underneath? A constant restraint? Don't press against me with that hug too hard! Might get an unwelcome erection. So brief hugs only? They become painful over time. A constant reminder of rejection.
Your comments though sincere, have an edge of emotional manipulation to them. You have not thought seriously about what your partner is going through possibly monthly, weekly or daily. Instead you are focused on YOU, on whether they may eventually up and leave YOU. YOU are getting you love life totally fulfilled, including foot massage, hugs etc. That amount of physicality is all you need to get your 'love language hit' so you get everything in the relationship.
The reason your partner feels 'everything is great' and there's 'no other place they'd rather be', is because you have probably (not maliciously, or deliberately, granted) done a number on their self esteem over the years and their sexuality. Sorry, but that is probably true. It is impossible to go through life with constant sexual rejection by a partner and your sense of self not take a massive hit.
If you were a woman saying 'my husband has barely touched me in 10 years and now says no more sex.. but I luuurrrvvvveee him and can't ever be with anyone else' you'd be told to wake the F up by all the women on MN who are frustrated by women staying in crap relationships. But MN loses all prospective when genders are flipped.
That said, as I said earlier, if they walked of their own volition into a marriage knowing the situation in advance with regards to how the sexual situation would be then more fool them.