The alternative was to announce "we now have 10 more planets, and there are probably a bunch more, and we'll probably never really get a definitive number".
That would also have had an impact on the public view of science. Perhaps not as bad, but it would have had an impact.
Planets predate modern astronomy. You have to negotiate with the public if you want to change what “planet” means. To most people, in most contexts, it means 8 or 9 specific things that they have specific ideas about, not a theoretical category of infinite objects.
No, the alternative would be to make up some latin sounding words for planets, dwarf planets, etc. and leave the vulgar planet alone to the standard 9 that we all know are planets.