Given that I think we pay like $7 a month for our phone line through 2Talk, it's not like it's a big financial burden - so even if the OP shifts VOIP providers there's some decent savings there.
A few years ago I would have said it was quite self-centred for people to expect others to only be able to contact them on a mobile - given the higher proportion that didn't have mobiles, or that calls to mobiles were charged per minute and were expensive (whether made from a mobile or landline). This isn't nearly the same issue given so many are on reasonably-priced plans with a set number of minutes, and often end up with more than they know what to do with (I have just under 2,000 minutes built up on a $16/month plan!).
That said, I think it depends on the specific circumstances. Some elderly in particular may be reluctant to call mobiles, whether due to a cost or simply sticking to what they know. I for one won't be getting rid of our landline, given my mother would struggle with calling us all on mobiles.
I also like it that a home phone is a collective device - it enables anyone to pick up, allows those who don't have mobiles (eg younger children) to engage and communicate without having to do so via an adult's phone.