I don't know why my tree is doing this, is it okay for it or not and if not what can I do to fix it. I do not mulch around the tree. It has been planted here 10 years now. It looks healthy, no issues.

Surface roots aren't a sign of poor health but crabapples don't usually have a problem with surface roots unless you aren't watering properly or your soil is impenetrable like clay. Do you deeply water the tree periodically or rely on lawn water? Crabapple roots are shallow but shouldn't be on the surface.

There is a fundamental conflict when growing trees in lawns because their watering needs are polar opposite. Roots follow the water. If you have relied on frequent, shallow lawn-watering and haven't been deeply irrigating your tree for the last 10 years, the tree roots have traveled to the surface to access the water. There is no correcting the situation now, but you can hope to encourage other roots to head downward by properly irrigating your tree going forward (not actually sure it will make much difference at this point).

The two primary disadvantages to shallow roots are tree instability if the soil becomes saturated by heavy rain or flooding, and reduced ability to withstand extended periods of drought.

I don't water the lawn at all, ever. I have an acre and a half so that's out of the question. I wouldn't care if the lawn all died to be honest
I have occasionally watered the tree (like a handful of times over 10 years) when we have had drought like conditions and the tree started looking like it needed it. We do get frequent rain where it just rains a little and then stops, not enough to water anything just to wet the surface. I do have clay type soil here, southern Missouri. It is on the east side of the house so has some shade on it by 4 oclock or thereabouts. The tree was only staked for the first couple years when it was small. I have never mulched it because I have some daff bulbs planted underneath. We don't mow around it until mid June usually so that foliage has time to die back. I do have a mole problem in this area and I have tried many things to get rid of them, nothing works so far.