I’ll start by making two disclaimers:

1. I am not remotely familiar with Atlanta geography or culture so please let me know if I make mistakes there.
2. San Francisco geography and cultural divides are very complicated and my opinion is that of a non native (though I’ve been here over 10 years) who has lived in Berkeley, Oakland, and San Francisco and notably NOT in the South Bay.

/disclosures

The big difference I see between your example with the braves and the 49ers is Atlanta is a major city surrounded by Atlanta suburbs. San Francisco is a major city surrounded by mostly water which is then surrounded by several other major cities, notably Oakland and San Jose.

This either cities have their own identities and cultures that are distinct from San Francisco. Collectively those three cities and the other around and in between make up the “Bay Area” so differentiating between a city and the Bay Area can be difficult.

The warriors (NBA) for example recently moved from Oakland. Across the bay into San Francisco. Very controversial. But they justified it by saying they are the “golden state warriors” not the Oakland warriors and they are the bay areas basketball team. Now that is very much open for debate and I’m sure most Oakland natives still have strong negative feelings about that.

On the flip side we have the San Francisco 49ers who are IMO Sam Francisco’s football team. For about 30 years they were not the only game in town and thus not universally the bay areas football team. Though very much open for debate considering the raiders were in LA, then Oakland, and now are gone. So moving them so far away makes me feel not like they are in a suburb of San Francisco but instead in nearly the heart of another city, San Jose. They are 8 molded from downtown San Jose and 40 miles from downtown San Francisco. San Jose is still very much Bay Area and they do not have another football team but I would imagine a large portion of their residents have been raiders fans for years (it’s just as far from the old raiders stadium to San Jose as it was from the old 49ers stadium).

As for being better economically, I don’t think the 49ers ever had attendance issues. They’ve been a very successful team historically I think the major economic driver was the cost to build in SF vs down south. While San Jose is by no means cheap, San Francisco is extremely dense and finding the space to build was probably going to be wildly complicated and expensive. The warriors managed to figure something out but I guess the 49ers couldn’t/wouldn’t.