This does not seem practical.
1) Checked baggage in the baggage compartment is packed more efficiently than storing in the overhead compartment because the greater volume makes it easier to fill holes.
2) Larger planes save money by loading checked luggage into containers, and loading the entire container in one go.
3) Only small bags can be stored overhead, so this scheme requires different handling for small and large bags, which is more expensive.
4) Using carry-on baggage compartments means baggage handling staff must be in the passenger cabin to load and unload. They will likely block passengers and increase loading time, which costs money. If the baggage is loaded before passengers board, then the ground time and therefore operational costs increase because currently the baggage is loaded in parallel to passenger boarding.
5) It increases passenger dissatisfaction to have their carry-on luggage further away, which encourages people to switch to another carrier.
6) How much extra space do you think there is? I've been on many flights where people had to gate-check their luggage because the cabin ran out of space. Think of the cost if 20 bags had to be gate-checked into the baggage hold because 20 bags had been moved to the carry-on section. (And airlines don't know precisely how much carry-on baggage there will be, because people can buy things after check-in.)