Can we do better than CCCV charging?
You should not exceed the maximum charge current of the cell, or the maximum output current of your charger, so you need a CC stage if you want the fastest charge. You can of course charge more slowly.
If you exceed the maximum voltage of 4.2 V on the cell, at best you dramatically shorten the battery life, at worst the battery catches fire. If you stop charging when you reach 4.2 V per cell, you haven't fully charged the battery by some margin, so you need a CV stage.
So if you want something less than a fast charge, to something less than full charge, you don't need to do CC followed by CV. If you want a fast charge to a full charge, without hammering your battery life, then CC followed by CV is the way to do it.