Syfy cancelled Stargate SG-1 because the network was pivoting to putting more effort into their other shows like Eureka which had a more general appeal. The writers snuck this cryptically meta exchange into S10E18 “Family Ties” poking at the network for how they felt the series was being mistreated.
In my opinion, it was a mistake to make seasons 9 and 10 of Stargate SG-1 instead of their original plan of making it a spinoff called Stargate Command. If they would have started fresh as (technically) a new series, I think it would have been overall better for the long term health of the franchise.
I didn’t say anything about quality. I just mentioned that they made a mistake in considering those seasons part of Stargate SG-1 instead of calling them a new show called Stargate Command. They wanted to keep capitalizing on the existing title that had become a household name. But that ended up being a poor decision that did not work their way in the long run. Stargate SG-1 was still prematurely canceled, whereas if it were called Stargate Command, it would have likely continued on for several more seasons.
I don’t think it would have. It’s not like they suddenly switched focus to the planetside operations instead of the teams, or brought an entirely new cast in to be the focus (like with Scrubs). They basically switched two actors out, but otherwise the show was roughly the same as it always was. Airing it under a different name would have hurt more than helped, as it would drive away die hard fans of the show and wouldn’t really bring in new ones as it still heavily relied on previous knowledge of the series.