What was the impetus of the orthographic reforms? Is there still a sizable contingent of Germans who use the old orthography?

To make the language easier to learn. Lots of languages go through orthographic reforms from time to time, English being one of the notable exceptions because there is no central authority that could impose rule changes in a way that would ensure that most language users eventually fall in line.

I entered school in Germany the very same year that the orthographic reform came into force, so I never learned the legacy spelling, but I certainly found it weird how much adult people at the time detested the rules that six-year-old me considered to be very reasonable (esp. the ss/ß reordering and the ban on fusing tripled consonants in compound words).

This is my very personal perspective. If you're interested in a more complete picture, https://de.wikipedia.org/wiki/Reform_der_deutschen_Rechtschr... looks like a good summary (through translation if necessary).

I know some conservative newspapers (Frankfurter Allgemeine Zeitung) kept using the old orthography for a while, but even they started using the new one in 2007, ten years after the reforms.