This is why this forum is great: good people sharing real experiences and academically correct info!
1. Multi speed pumps, especially high end ones, work as described above with superior windings, seals, bearings, and 3-phase electronic convertors. But they are crazy expensive.
2. Up-sizing the plumbing is key (but not helpful in existing pools). Up-sizing the filter helps a lot (but some filter/pump combos need a minimum back-pressure. Cartridge filters don't have this requirement). Most of the wasted energy in most pools comes from "dynamic head" (friction resistance) followed by pump design.
3. Return on investment is best with the smallest pump running 24/7 with the biggest filter and plumbing. Any simple pump so configured to do 1 turn over per day will be the cheapest long term option.
4. Unless one does careful static/dynamic/pump calculations, it can be hard to know exactly what pump to buy. I know that I had the wrong pump for 5 years! Bigger is not better (too much dynamic head = wasted energy, accelerated wear on pump and plumbing) and too small can be worse.
5. A variable speed pump, even if only used during initial set-up, can give you all the dynamics of the pool. You could then just buy the pump you really need. A word of caution: most pools will be fine with pumps which traditionally would be considered "too small" but they are very hard to find. Thus the variable speed pumps.
6. The pool described above, even with the new pump, probably still has more flow than needed as 30gpm should give 2 turn-overs per day. You might consider a timer too.
7. MY pump is a Pentair IntelliFlo (3.2kw, Variable). It was CRAZY EXPENSIVE at over $1000. However, I am crazy. My pool has a salt water generator, a roof top solar heating system, a lilly pad (kinda like a Jacuzzi, sorta), and an air source heat pump. Under differing conditions (such as automatically directing the water to the roof top collectors), I needed a pump that could vary speed to maintain a set gpm output. There are lots of fancy controls out there, some pretty complex, some not compatible. Or, one could just connect the IntelliFlo and read the owners' manual. Yep, it can do all that right out of the box. No required add-ons or gizmos.