So a few years ago when I was getting on a kick with other Canon 5d2 cinematographers, I did a deep dive into the subject of trying to collect parfocal zooms. As has been mentioned, cinematographers want to be able to zoom while shooting, maintaining the focal point constant, so a varifocal zoom is effectively useless. The cheapskates among us wanted to use still camera lenses for this purpose, which introduced a whole new set of headaches I won't get into.
What may interest you in what I've gathered is that in the early days prior to autofocus, parfocal designs seem to have been fairly common among the incumbent camera and lens manufacturers. This predates me as a photographer by some decades so please keep me honest here, but I understand that what photographers wanted to do when they had to critically focus was to zoom all the way in, nail the focus, then zoom back out to compose as they saw fit. I think camera manufacturers designed their zooms with this workflow in mind. Leica Vario-Elmar-R lenses are one specific example, which has had a lot of attention as Leica R is one of the mounts that easily adapted to Canon EOS used by this 5D crew. I once had a Tokina close focusing 35-105/3.5 manual lens in M42 tested as parfocal enough for 1080p video. So the data fits the theory. You can google for parfocal lenses for your system if you must have one, like this one for Pentax
https://www.pentaxforums.com/forums...cussion/201887-list-parfocal-zoom-lenses.html . I gathered many if not all of the Canon FL/FD pro zooms were parfocal as well (my FD 35-105/3.5 copy is), with the FD 50-300/4.5L being parfocal and particularly sought after, with street prices around $1000.
Most Vivitar series 1 zoom lenses were a well publicized counterexample: they made public claims on how much sharper (possibly lighter?) their varifocal lens designs were, leading to some early confusion when they were introduced from new users on their first few rolls to discover they had made mistakes on critical focusing.
Much later when autofocus came about, there was no longer any need for the parfocal optical design since photographers generally relied on autofocus, so the tradeoffs mentioned by others on this thread no longer made sense. There still were some holdout zooms for reasons I can only speculate. I can confirm in my tests that the non-IS Canon 70-200/2.8L I bought in the late 90s seems to be sufficiently parfocal for my needs when mounted on the various Canon digital cameras. Perhaps with this lens, it was a desirable feature for sports photographers who wanted to be able to work quickly, or was it a continuation of an FD design?
Lensrentals wrote about the subject in 2011, as they deal with only new lenses.
https://www.lensrentals.com/blog/2011/02/photo-lenses-for-video/4 and later sort of contradict themselves later by saying there are no parfocal zooms any more
https://www.lensrentals.com/blog/2016/03/mythbusting-parfocal-photo-zooms/
Again, perhaps someone who was avidly in the 35mm stills scene in the manual focus era can speak up if this rings true.