Why are HX machines so popular?
Not to answer a question with a question but, "compared to what?"
If I read your post correctly you're asking "Why, after a certain price point, does the HX design drive the "switch to steam" design out of the market?" The answer is contained in the question, and Dan got it right away. The answer is steam. Instant steam in (small) commercially viable quantities. No back and forth between brew and steam. No two minute wait.
If you look at ad copy for some of the first HXs on the popular market, like the Pasquini Livia 90, you'll see that the copy writers set great store to the machine's ability to brew and steam simultaneously. There's also a certain amount of snob appeal in play. As the popularity of espresso spread in the US, you actually saw prosumer HX machines in small restaurants and bars (still do, too!), they seemed more professional, and hence more desirable. Do I sound disapproving? I don't mean to. That's part of my decision making process as well. When you're spending more than $1500 on a glorified coffee pot it's nice to have some validation from the big boys.
Double boiler machines, fairly new on the market, start at close to $2K, go north from there, and solve the steam problem more elegantly than HXs. The design also promises (and I stress the word promises) to reduce some of the problems with inconvenient temperature control. But they're expensive, and except for the Reneka, which is poorly distributed in the US, haven't had time to develop a following yet.
[Well paraphrase really.] What's up with the E-61?
The E-61 group was originally designed by Faema for commercial use. Driven hard, it's got a great thermal stability. Because of mass and design, you can bring it back to appropriate temp quickly after a resting period, and the pre-infusion feature is a wonderful thing. The kind of temperature accuracy that the gentlepeople of this forum talk about was unknown until fairly recently. The E-61 wasn't designed to hit brew targets with 1/2 deg C accuracy. That it can, even though requiring an elaborate "water dance" or a humongous boiler, testifies to the strength of the design. [Can I get an Amen?]
Other important pre-purchase considerations besides the group include boiler size, thermal mass, pump type, quality of other components like the pressure stat, availability of parts and service, etc. Things bing what they are, we're going to have to add energy efficiency to the list.
Back to the group, there are other designs which perform as well as the E-61.
Rich