I think it is weird to be in a relationship where one person drives, one doesn't, and the non driver never ever benefits, or expects to benefit, from the driving. So weird, in fact, that I do not believe anyone is in one, or at least not in one that is normal and caring and loving in every other way.
People live different lives to you. Sometimes, those lives involve not relying on cars. You can find that as 'weird' as you like, but it is nevertheless true.
But you also think it's "odd" and illogical to want to split the life driving load where possible.
No, I think it's 'odd' to be all up in arms about non-drivers 'expecting me to do all the driving', when plenty of non-drivers expect their partners to do less of 'the driving' than you expect yours to do.
If driving is that much of a hellish chore for you, why not rearrange your life in a way that requires less of it? Totally possible. Many of us have, either through choice or through necessity. 'Weird' though it may be to you!