We could, but it would have broken compatibility with v4 just as thoroughly as v6 did and so would have had the exact same deployment difficulties v6 has.
In fact v6 mostly _is_ a minor tweak to v4; most parts of it are lifted directly from v4 but with a longer address.
The larger address space is only an advantage if we don't need a v4 address. The situation "I need a v4 address" is not worse than the situation "I need a v4 address and a v6 address".
Not exactly. There's some pretty snazzy interoperability tech out their. (I.e. 4-6-4 XLAT) that let's clients get v4 addresses when they need them, which means if there's a big chuck on devices on both ends that support v6 you don't need as many v4 address.
This kinda a problem for motivating people to move to v6 because as implementations of v6 grow there's going to be less and less pressure on the v4 address space.
(Which we could have had with a minor tweak of IPv4 instead.)