We need more shooters that are not live service games. Wolfenstein as a franchise has been the one that's refused to be a live service game and The New Order and The New Colossus were good. Mass Effect 3, while it's campaign story was polarizing, was beloved for its multiplayer. Perhaps the Bioshock sequel coming [waves hands in the air] will fill that void, but that's a lot of hope to hang on to one game whose last entry was... a source of great division.
If I were to make a game to save the FPS, I'd make it original IP level-based shooter. I'd set it in a fictional place, fictional time with maybe some aesthetics that callback to the real world but nothing so specific as to make it messy. I'd make three versions of the main character: standard dude, standard lady, and a nonbinary character (similar to the way Assassin's Creed: Valhalla did it). Everybody gets to see themself or something close to who they are in the main character. Most crucially, it would receive patches and maybe updates to improve upon existing features, but it would not be a live service game. No purchasable cosmetics, no DELUXE PREMIUM ULTRA RARE EDITION for half your paycheck plus a second mortgage on the house, and no content locked behind add-on packages.
The plot: You are a bounty hunter tasked with hunting rogue machines. They could be something as innocuous as a house cleaning bot that's gone AWOL to a lethal corporate security drone (inspired heavily by The Murderbot Diaries by Martha Wells and maybe a little of the Wayfarer Series by Becky Chambers). The first third of the game is pretty standard bounty hunting when, uh oh, a mission goes sideways and now you've been captured. Turns out the bots going haywire wasn't an accident. The machines have been liberating each other. Now you spend the second third of the game escaping. In the final third you get to choose whether you'll turn on the humans and side with the machines or side with the humans and shut down the bot liberation movement for good. Either way the ending will be bombastic, promising an escalating challenge for even the most skilled of shooter players.
Then you develop an expansion, either based on a minor character (think Dishonored: Death of the Outsider) or expanding out from some little thing that was implied but never seen in the base game (think Mass Effect 3's Citadel, From Ashes, Omega, Leviathan expansions; Mass Effect 2's Shadow Broker expansion). People still talk about Mass Effect's expansions because they were so high quality and added so much value to the play experience (admittedly, there were a few that sucked).
Shooters have all but been decimated by the live service model. That's not to say they're all bad, but they don't play the same. You can never get closure with a live service game. I'll never get closure playing through Fortnite missions. Hell, people are still grinding out stuff on Destiny 2 despite the fact that the final big content update happened a few months back. It doesn't seem like folks who invested in the narrative for that game got any real closure. Maybe we can't go back to a time when all shooters were level-based, but honestly I think one or two good ones from time to time would do the game industry some good.