This cherry tree was about this size when we moved in more than 2.decades ago. It seems in decline. I thought cherries lived a long time? Or do they just have some cultivars living longer than others? I think I may take it down if this keeps up. I understand cherry wood is desirable for roasting duck in the bbq? I really like this tree. Maybe because it blooms early and pretty and is my main harbinger of spring around here.
It definitely depends on the cultivar and rootstock, and local conditions. Wild cherries live longer and grow bigger than domesticated ones. I have sweet cherries that are full of vigor at 25 years old, and a couple that are nearly dead at 12 years old (on dwarfing rootstocks). I have a tart cherry (Montmorency) that is doing very well at 25 years old. Your cherry looks wild, to me. Mainly because of the size, although sweet cherries can grow pretty big - that's why they have cherry pickers. As for your question, I think you should lose your cherry when you fell ready. Meanwhile, how about growing another one, anticipation its decline? Also, with tornadoes around, at least there isn't a house within falling range of your tree.
I would give it a good pruning. Maybe reduce the branches by a third and remove the crossing branches. This may (or may not) invigorate it. Then see how it does next year. I'm always for giving stuff a chance before deciding to remove it. It might have just reached it's mature height and needs fertilizing and pruning.