adopt a Harvard type tuition program where your parent's economic status will never keep you out if you have the qualifications. But how many US based Mormons are really in the bottom tier economically? Probably not that many. Outside of the US that is a different story and thus you have the PEF and Pathways to help them along.
Sadly, well maybe, I don't see BYU doing anything about this as they have addressed it with BYU_I and Pathways.
I however am grateful that I did come from a very low income household and mad it to the upper middle class.