As mentioned, the problem with the OP's proposal—or any variations on it—is you still have at least one finger going just as fast as it would be with using 1-2-1-2.
I am a big fan of using three fingers. I don't always—often two, and sometimes just one. But it's nice to have it in the toolbox.
I read somewhere that Sheehan actually forces himself to put an accent at every first downbeat, so that he doesn't sound like playing triplets all the time.
So it sounds like 3213 2132 1321 3213… instead of 321 321 321 321 321 3…
This. This is no different from how we all learn to play triplets as 1-2-1 2-1-2 1-2-1 ... , just a bit more complicated. This is essential to getting eighth or sixteenth notes at all even with three fingers. I need to practice each pattern individually:
3213
2132
1321
to get each down. And when putting them together in practice, I need to exaggerate the accent:
3213
2132
1321 ... I don't do that when I'm actually playing, but I need it in practice to keep things in fours.
It can help to work just on twos first:
32 13 21 32 13 21 32 13 21 32 13 21 ...
I am no Billy Sheehan, but I can definitely play some things this way I would struggle with with only two fingers.
I find, for me, it is helpful not only for sheer speed, but almost more for endurance. A steady sixteenth note thing that would wear me out 1-2-1-2 can be sustained much longer with three fingers.
A side benefit of getting my 3 working is that then I can switch with two-finger when needed: if I get tired playing 1-2-1-2, I can switch to 1-3-1-3 or even 2-3-2-3 without anyone catching on.
Actually, the one thing I will NOT play with three fingers is triplets! I find it too hard, playing with three fingers, to avoid slipping towards two sixteenths and an eighth. That is, rushing the 321, and having the 1 note last longer than the others.
And yeah, agreed with others that often the most efficient thing is to just improve your two-finger speed, especially by relaxing and by dropping your thumb. Or just using a pick. But the three finger thing is worth the effort learning in my opinion. It opens up a lot of options.