With the proviso of all other things being equal, yes, I would say that spoke strength is the most important factor to strong wheels. Think about what "kills" a wheel. Wear out a rim and you can replace it with a rim of equivalent ERD. But if you break only a few spokes...especially 2.0mm and thinner...and the wheel is toast. (Breaking a hub is a different story but thankfully rare.)

I have said this numerous times in the past but it is possible to build a wheel out of the strongest rim that you can find...a steel one...and the lightest spokes you can find and you'll have a positively awful wheel.

Yes, the number of spokes matter. Even with a stronger spoke, a 28 spoke wheel is going to be more prone to spoke breakage than a 48 spoke wheel, especially if the bike is carrying more load. That's the reason people have gone to such high spoke counts. But the triple butted spokes do increase the resistance to breakage significantly which means you can build with fewer spokes. In the day and age where high spoke count rims are rapidly disappearing, that a plus. 48 spoke rims (and hubs) have always been rare. 40 spoke wheels are equally rare. With disc hubs it's even hard to find 36 spoke hubs and there are fewer 36 spoke rims to go along with them.

I wouldn't ride them personally but building a 20 spoke wheel with triple buttes spokes would be at least the equivalent of a 24 spoke wheel, in my opinion. I don't completely agree with Hjertberg that it's the equivalent of 10 extra spokes but, I suspect, it's higher than the 4 extra spokes I give it.

As to the type of spoke, I'm not a fan of straight pull...not may people are if you go by the availability of straight pull wheels. I find them difficult to build with because of the twist when tensioning. I realize they are probably stronger but getting the tension high enough to take advantage of that extra strength is difficult. There is also the proprietary nature of most straight pull spokes and wheels. There are lots and lots of straight pull wheels out there that are basically useless because you can't replace a broken spoke.

Carbon rims just aren't something that I've personally worked with. They are too expensive. Frankly, I haven't even seen one yet. At the current price of carbon fiber, I don't expect to see the price come down much in the near future, either. Even if you could reduce the price of the raw fiber, the material still involves a lot of hand work which is expensive as well. They could be great rims but at this point they are out of reach of most wheel builders.

Yes, wheel builder skill is a factor and it's important. But a triple butted spoke is more forgiving than other spokes. A new builder would benefit from using a spoke that takes more to break. If you undertension a double butted spoke, it is far easier to break than an undertensioned stronger spoke. The nature of the tighter fit in the hub also makes for a slightly stiffer wheel so an undertensioned spoke won't flex quite as much which means it doesn't break as easily. Bend a thin wire vs a thick wire sometime and see which one breaks first.

Basically, a new builder building with triple butted spokes will build a better wheel and have a better experience for their first few wheels. The failure of your first few wheels is probably the worst hurtle to get over as a new wheel builder. I'm a stubborn as a Missouri mule...I get it from my Grandmother...so I just stuck with building until I figured it out but many people give up much earlier than I would.