Unfortunately, no. The spacing of the bins (each of which can hold 3 legal-sized carryons) is fixed, while the airlines continue to shrink the seat pitch in order to cram a few more rows into coach. That can create a situation where there are more seats in coach than there is bin space for overhead; it's not one bin slot per passenger. And then there's the matter of the bulkhead and exit row seats which generally don't have any under-seat storage, so ALL of their items have to go overhead. As I recall reading, there's only enough overhead bin space for about 75% of the economy class passengers' full-sized carryons (if everyone was carrying a carry-on as well as a personal item).

The airlines created this problem by incentivizing people to carry on while simultaneously reducing the amount of overhead space available on a per-person basis. The way to fix it is to flip the current fee structure so that carryons cost money while one checked bag is free, and to improve in-transit security and timely delivery of checked luggage. But the airlines aren't going to do that: that would cost money, and every bag stuffed in an overhead bin instead of being checked frees up some room for more-lucrative commercial cargo in the hold.