"Switching power supplies work at range of voltages." They work at a range of voltages they are designed to work at. The larger the range you want to support, the more it will cost in the design (in $, size, reliability, etc). It's one thing to make an 80W laptop supply work across 100-240V, but it's quite another to do the same for a 450W ATX supply, and the benefit to the customer is much lower.
[Update: this paragraph is speculative and wrong:]
The switch likely rewires the primary in the transformer so that the regulation circuit doesn't have to work over such a large range.
[Update - comment added after downvotes:]
OK, I've been voted down. The 2nd paragraph is speculative and wrong , so I won't protest.
I am well aware than SMPS transformers don't run at line frequency, but I wasn't aware that you couldn't still have a split primary with a switch on that transformer. And the schematic was not up at the time.
My ignorance of that doesn't invalidate the main point - the switched voltage doubler still serves to reduce the range over which the supply needs to adapt automatically. So that brings me to a question: is it not harder, in terms of cost/efficiency/reliability, to make a PSU that can adapt over a 1:2.6 range as opposed to 1:1.3? And, does not the tradeoff become more significant with higher power? As long as a PSU with a switch is more efficient & reliable than one without, I'll take the one with a switch for a desktop. @johnfound answer says that modern PSU are univeral without a switch - that's absolutely true for wall warts and laptop supplies, but most ATX supplies have switches.
So it's a good question, and I believe my first paragraph is a good answer. But I'm prepared to learn more.