Reminds me of the extensive discussion of "animation cancelling" in Genshin Impact. You can't accelerate the start of an attack, but you can cancel the animation between that and the next one, and this is apparently quite important for some characters.
For Claymore characters it's usually quite helpful to hit either 3 or 4 times (I don't exactly remember) and then dash to the side to prevent waiting ages for the animation of the final attack to complete, otherwise you wouldn't be able to start attacking again.
Star Trek: Bridge Crew comes closest to what I'm talking about. Imagine that but not VR (well, VR is cool for this, but I don't have a VR headset, so...) but more of a Firefly type of atmosphere.
There was once a UDK demo or sample game that mixed FPS with space combat that was cool. Each player on a team started in a large ship, which someone could fly and other team members could control cannons, or run around the ship, or get into single-person fighters to attack and board the enemy ship. I don't remember what it was called, just that I got it as a sample when downloading UDK way back when it was still a thing. It was pretty cool!