Given that we know CDPR can deliver legitimately engaging close combat
Arguable.
I'd rate W3, their best melee combat game, as merely "Passable" combat. Simply good enough to let the world keep a player interested. With W1 and W2 having pretty bad combat (W1 being so bad I could never actually finish the game)
Meanwhile, you have games like Chivalry, Morhau, Deliverance which do offer engaging and deep melee combat. In first person.
It's not the perspective that makes or breaks melee combat. It's the time put into it. CP2077's melee combat isn't bad because it's first person. It's bad because the main focus was on gunplay and melee took a back seat so it only has a rudimentary system in place.
As far as flashiness... Nothing about first person prevents some level of flashiness. Games like Red Steel were pretty flashy and cool (Albeit using the Wii's motion controls) but even things like Metal Gear Rising can have its flashy cool melee systems adapted to first person perspectives.
You might argue that first-person has parkour, well I'm going to say that the parkour could be way better than it is.
Parkour is not limited by first person perspectives.
Mirror's Edge is one of the premier parkour games to ever exist and is a first person title.
It again simply comes down to spending the resources on implementing it. CP2077 simply forwent parkour systems.
Cover mechanics can function in first person perspectives. There's literally nothing stopping them from functioning.
The singular thing you are incapable of doing that third person is, is the blindfiring where you shoot (With useless amounts of inaccuracy) without exiting the cover. Which is a feature that is 99.99% of the time, completely irrelevant (The only niche scenario for it is if some large target is directly on the other side of your cover so you can dump bullets into it without need for accuracy)
So if you don't have a HUD to tell you how much ammo you got, you can upgrade your gun to have a little holographic ammo counter, things like that.
Umm... Things like attachments to guns to have ammo counter generally wouldn't work very well in a third person perspective where your camera won't be particularly close to your gun...
Sure, you could try and make it work with novelty oversized projections or weird ADS camera angles... But that kind of thing would work far better in first person perspectives (Which is why games in which you have ammo counters on guns are all FPS while all TPS rely on HUD's for that information)
I say this stuff as someone who generally perfers third person over first person perspectives. There's little actually limiting from using first person perspective in general. It mostly comes down to how well a developer decides to implement features.
While first person DOES inherently have some immersive benefits over third person since you are literally seeing through the eyes* of the character. You see what they see. Things like drunk effects and visual impairment makes more sense. When you look around, your character is looking there too (So characters can react to say... You staring at their breasts...)
*Technically, first person perspectives put you in the character's chest in terms of hitboxes and when accounting for where hand positions are... The only exception to this is being able to see your full body when looking down.