With any American created MA, it makes sense that English is spoken.
In judo or anything from Asia, it makes sense to learn it with the technique & descriptors in that language. There are a bunch of reasons, but IMHO I'll hit the high points in my book:
* Continuity
* Portability
* Respect
* Negating "Lost in Translation"
On continuity -- You don't rename what's already named. You don't apply a new label to something that is already adequately named. If it wasn't adequate, it would've been named differently earlier on.
On portability -- You can train in other schools of the same art & everybody's on the same page. I can go to any other CLF school in the world and if the sifu calls (for example) "gwa choy sei ping ma, sow choy ding ma, chop choy sei ping ma", I know exactly what to do & how. It doesn't matter if I'm in China, Russia or the Bahamas, the cohesive glue of the same language used for teaching makes portability a non-issue. The Judo you mentioned would be the same. Go to any judo club in the world & everybody calls the techniques the same name.
On respect -- The head of our organization is Chinese... his teacher was Chinese... his was... etc.... It'd be one thing if this was his creation & he decided to use language "X", but it's not. It's a 200(+/-) year old CMA from China. Chinese was spoken when it was developed & first taught in China, so it should be too now. For example common example would a restaurant.
You go to a French restaurant, you want to see "Es'cargot" not "Snails" or the like.
On Negating Lost In Translation -- There are words that have a specific meaning or value in their native language that when translated, loose something. Something here. There are feelings, or energies that go along with certain names that can't adequately be described or are described with 20 minute lectures. I don't know about y'all, but I don't have time in my class to lecture for 20 minutes about a chaap choy. I say it, demonstrate it on the air & a target, give a brief explanation & go. Why try to fix it if it ain't broken?