Pretty much will echo what PoolBoy says.
The BBC do occasionally mention tournaments other than the ones they cover, so there obviously isn't any kind of rule telling them not to. However when they do discuss other tournaments, they tend to gloss over them a bit making them sound trivial and unimportant.
This may be deliberate on the part of the BBC, but is also due to what PoolBoy touched on his second point. A lot of the commentators are woefully misinformed about the professional game.
I watched an episode of Question Of Sport with Dennis Taylor on, and he too was clueless when it came to the snooker questions. And I mean clueless. There were several about snooker. (They try to add questions that are about the sport the guests participate in.) One question he was asked to name a Crucible finalist whose surname began with T. He sat there looking baffled for a few moments and then went; "Oh, I was one of them."
Literally, he struggled to answer a question about his own World Championship winning performance. (That the BBC have been mentioning every tournament since.) He didn't get any of the other snooker questions correct at all.
I suspect it's a combination of both the BBC blase attitude, and commentator laziness/dislike of watching televised snooker. If their employee doesn't care that they know nothing about a sport they are paid to be experts in, why should they bother to keep themselves informed?