The button provided a two-fold purpose in it's original day.
In the days of the IBM PC-XT, the first of the clone/competitors was Compaq. Rather than simply clone the original machine, they changed the clock crystal and doubled the performance from 4.77 MHz to a blazing 8 Mhz. (hey, when's the last time you saw an increase of THAT magnitude!!!)
As noted, some of the early programs were timing critical (like FORMAT.COM) and messing with the clock simply caused problems. An easy fix was the Turbo button - which slowed the machine down to the original 4.77 Mhz. Armed with that, all programs worked.
On the flip side, Compaq (and all later clones) used it as a marketing tool, showing with one flip of the switch how much faster than IBM that THEIR machine was.
Just a side note - when IBM users found that for a couple of bucks, they TOO could double the speed of their machines by changing the clock crystal, IBM retaliated. The BIOS was re-written to time the length of the POST process. If you POSTed too fast (with anything but the original clock chip) - the machine shut down. IBM figured that you were getting too much performance for the dollars you had spent -- and were too close in performance to the next level of machine.
The early days of IBM were an ongoing story of limiting the user.
Hope you enjoyed the trip down memory lane......