I could not do it with only 3 powders without giving up a significant amount of the utility of many of the cartridges I load for.
I would need at least 2 different powders for rifles and two for handguns. I need at least two, for each, one fast/medium and one medium/slow to get the full range of performance.
If I chose a fast pistol powder, like Win 231 or Bullseye, I can't get full performance from my magnum pistols. If I chose a slow powder like 2400 or Win 296 they are not suitable for my small pistols rounds,, the best compromise for me would be Unique, which I do already use in many rounds, but Unique can't quite deliver top end magnum performance. For everything else, its does pretty well.
And a similar situation holds with my rifles. I load for over 30 different rounds, rifle and pistol in calibers from .22 Hornet up to .458 Win mag. There is no ONE powder suitable for full performance over that entire range.
2 powders will cover MOST of it, but you need 3 at least to get everything each different round is capable of.
If you can show me 3 powders that between them offer full power performance in cases with charges ranging from 2-3gr to over 70gr of powder rifle, pistol and shotgun, I'd be interested in hearing what they are.
Lots of combinations of powders will cover MOST of that range. I can't think of any that will cover the entire range to the fullest.