This is a tricky question, because the financial aid system can create odd incentives.
Good schools tend to price themselves above and beyond any reasonable middle-class ability to save and then offer financial aid, much of it in the form of internal "grants" or "loans". If you think about it, the internal grant is more of a discount than a grant since no money need have ever existed to "fund" the grant. The actual price to the parents is based on financial aid paperwork and related rules, perhaps forming a college price-setting cartel. It is these rules that need to be considered when creating a savings plan.
Suppose it is $50k/year to send your kids to the best school admitting them. Thats $200k for the 4 years. Suppose you had $50k now to save instead of $10K, and are wondering whether to put it in your son's college savings (whether or not you can do so in a tax advantaged way) or to pay down the mortgage. If you put it in your kids savings, and the $50k becomes $75k over time, that $75k will be used up in a year and a half as the financial aid system will suck it dry first before offering you much help. On the other hand, if you put the $50k on paying down the mortgage [provided the mortgage is "healthy" not upside down], your house payment will still be the same when your kids go to college. The financial aid calculations will consider that the kid has no savings, and allocate a "grant" and some loans the first year and a parental portion that you might be able to tap with a home equity loan or work overtime.
Generally, you should also be encouraging your kids to excel and perhaps obtain academic scholarships or at least obtain some great opportunities. A large college savings fund might be as counterproductive as a zero fund. They shouldn't be expecting to breeze through some party school with a nice pad and car, homework assistance, and beer money. Unless they are good at a sport, like maybe football -- in which case you won't need to be the provider.
It is not obvious how much the optimal ESA amount is. It might not be $0. Saving like crazy in there probably isn't the best thing to do, either.