This is purely my opinion/anecdotal observation, but I suspect a lot of these slowdowns are the game talking to the EA servers at certain points and waiting for the server to update. I've had a Samsung 840 EVO SSD in my PS4 since launch and exiting games is still pretty slow.
Why I suggest this, is because even just logging into the EA server takes ages for me, and always has in most other EA games (Mass Effect 2 on Xbox 360, Dragon Age: Inquisition on PS4, etc.). The time DA:I takes to log me in seems to be the same on the 113 Mbps cable connection I had until August last year as the 3.5Mbps ADSL connection I'm on at the moment, so bandwidth doesn't seem to be the issue.
The Battlefront menu takes around 10 seconds or less to appear after launching the application but logging into the EA servers can take a couple of minutes.