Thinking about EA (or any big publisher) as a monolith is quite counterproductive to generate a mental model. In practice it is several studios with an overlord. Some studios might still be independent enough that the overlord just stays out of the way.
While that's true, there's also often a noticeable trend of games moving in a similar direction across a publisher - for example the disastrous live service attempt from Bioware (Anthem). Whether this is due to top-down pressure or just corporate vibes or culture, publishers definitely seem to have an impact on what kind of games get made.
I believe that Battlefield 4 was the last good Battlefield game. Biggest asset was fully self-hostable servers that provided progression, community control, and allowed gaming clans/organizations to actually community-build. Nowadays, forced matchmaking and limited party sizes really eliminate the ability to build large communities.
The consolidation of publishers/developers in controlling all of the online experience has started limiting online gaming's ability to be a reasonable third place.
BF4 was broken on launch, with servers crashing from people simply playing the objective. These studios have been serving people garbage for close to two decades by now. They deserve their fate.
Battlefield was always jank built on top of an innovative (or just finally achieved) idea of large battles with vehicles that worked. 1942 wasn't really innovative but the technical achievements of player count and not shitty vehicles made it a novel experience.
The further they moved away from that, the more generic it became. I don't want to say any one was really the "last good one" but the last one I put significant time into was BF2 but I played all pc versions up to 4 and you're right, it was absolutely broken on launch. It's not why I haven't played one since but I never did go back to BF or even really FPSs since. They all seem like CoD clones now, even (or especially) the CoD franchise and it's tiring.
BF4 was a massive redemption story. It started rough, yes, but it went on to become probably the best sandbox shooter ever released. Sorry if you didn't have the patience to make it through the initial 6 months. You missed out.
As much as I love bf4, I will say bf1 really hit it out of the park. It was a fantastic game that ran well at launch and basically only got better with the dlcs. It's servers also seem to be immune to a ddos that regularly kill bf4 servers.
