You ask questions in such a way that it's difficult for most people to know if you are being naive, or sarcastic, or trolling etc.
Let's start with "ignorance is not a sin, and it's easy to fix".
On the other hand, ignorant people often ask questions in a different way, that doesn't sound confrontational or defiant.
What often prevents people from responding is the impression that we have that some people think that engineering, history and technology, among other things, are completely disconnected from each other or, if they are weakly connected, the connections are unimportant.
Quite the contrary, what technology and engineering *can* offer is more often than not very strongly connected and can't be pried away from each other, and knowing what happened when and why (History) is very important.
So, to get to the point, burners with multiple (2 or more) resistors which were controlled by switches that would turn one or more in different combinations were not exactly "chosen" over infinite switches any more than open coil nested in a ceramic disk were "chosen" over Calrod or cast-iron burners.
Things like that can only be "chosen" once they get invented, perfected and ready to be mass manufactured, and even then, now you face a market that is used to another way of doing things, and there might be a ton of clients that might not be so eager to switch and learn new habits.
Even when the change is genuine improvement.
When "sealed" coil elements (Calrod, Corox etc) showed up, people who could afford them and recognized them as a big improvement, still needed to learn new skills. Look at old user guides, and they were filled with suggestions on how to control the heat for elements which had a very large inertia to temperature changes, and Calrod style cooking was much simpler than the original elements.
Sooner or later, Calrod-style elements became inexpensive enough and attractive enough for people to demand them instead of open coils which could shock the user or cast-iron burners that took longer to warm up and cool down.
Infinite switches came much later. In theory, the idea was simple, and there *were* some switches like that used in laboratory situations, where the clients *needed* stuff like that and could find someone to fund switches that cost more than 20 bucks per switch, and even then, they were not reliable enough to be used in heavy duty situations by people who did not read the user guides nor would be careful, they were used in special situations only.
Eventually, when it became feasible to produce infinite switches in mass quantities and inexpensively, they became an option, and, even then, there were people who were used to the 5 or 7 position switches that did not jump to adopt the new style.
In any case, the answer to you question(s) is that, historically, infinite switches and one-resistor burners came into the scenery rather late, cost more to produce until they got perfected, and then they had to deal with a market that was used to another system.
