Also in this case if you want to help someone to keep property they cannot afford then maybe tax assessment reduction should be based on new owner's income level and not on a year deceased relatives bought place

If we're against someone being priced out of their home by taxes, wouldn't we also be against homes being priced out of families by taxes too?

Why? I'm totally fine with a measure that helps keep fixed-income residents in their homes when property taxes would otherwise eat them alive. I see no reason why we need to keep that property tax burden affordable when that resident passes away and the property goes to their heirs, who presumably already live somewhere else, paying taxes they can afford. If they can't cover the newly-assessed property tax on their relative's residence, then they should sell it and stay where they are.