Is it best to just cook with the oil that has the highest smoking point?
The smoke point of the oil is only one factor.  It is advantageous in some types of cooking (particularly searing and deep frying) to have a very high smoke point.

Cost is another factor; the high smoke point oils are often more refined (getting rid of the elements that smoke) and are therefore more expensive.

They also don't contribute flavor the same way something like (unrefined) olive oil will do.

Most importantly, however, they will not really save you any effort on cleanup.  You still need to wash your pans.   They may be somewhat less likely to polymerize on into a hard film during routine cooking, but that should not happen in any case.