I agree with your analysis on hardware performance vs server lag but it does seem that the problem happening on all platforms PS4, PS4 Pro, XBOX and PC, see the link below, and that DICE and EA have acknowledged but are at a loss to fix. Or the issue is so fundmental that significant code change is required,
https://www.gamespot.com/articles/star-wars-battlefront-2-experiencing-lag-issues-on/1100-6455211/
I noticed the the frame freeze issue appears to be much worse at the weekend when the server are likely to be under more load from players than in the week .
Last night (Friday 8th Dec) Battlefront II was pretty much unplayable on the standard PS4, too much jitter for a Specialist and close combat meant instance death as constant freezes left you open to attack. The frame freeze on respawn was horrendous with pauses for 2-3 seconds on almost every respawn. I love Battlefront and the PS4 but yesterday I was ready to ask Sony for my money back.
I presume the ”Fall Back” feature is required in order reduce the size of the maps that need to be processed by the hardware which would suggest the developer are pushing the hardware limits. This does make the maps feel at lot smaller and Battlefront I and prevents player from holding back or pushing forward to pick of targets.
In conclusion this frame freeze looks like a combination of hardware performance and server lag hence it being worse on PS4 than on PS4 Pro at peak times and affecting all platforms.
I appreciate this would make for a difficult job for the developers to debug hence the recent patches having little or no effect. It would be courteous though to have some formal feedback from EA and DICE updating us on what is being done before there is a mass exodoeus from the game as players give up..