When a pickup sits to close to the strings the pickup can become demagnetized over time reducing it's output. Same thing if you rest your guitar facing against a loud speaker. Many 30~50 year old guitar pickups have lost 30% of there output or more.
Low action is inspiring. It makes you want to play faster. However it can have a negative impact on the attack portion of the sounds adsr. With speed playing and tremolo bars there is always a trade of for bend range and action. Higher pickups can also cause unwanted compression in your tone. Softer attacks are less articulate, In short you'll have less nuance transferred from your technique to the output jack. This may not seem important if you are a speed metal player but is important if you play any other style where playing dynamics are important for emoting.
In regards to string action there is also a portion of the equation often lost,Fret Height Fret Height can also affect clarity of tone. I've got two telecasters with near identical neck specs and identical action. All the measurements are exactly the same except for fret hieght. On my Pinecaster (Modern Player) it has standard jumbo frets. On the Blacktop (vintage modified) it has medium jumbo frets. The medium jumbos are raised higher then the standard jumbos. Even acoustically the differences are abundant. The pinecastet is easier to play.It's easier to play "stretch chords" it's easier to play octaves, it's an easy grip guitar. The blacktop rings out more clearly.most notably the hammer ons and pull offs ring out more clearly.
Brighter, punchier more harmonic overtones. Note this is a side by side comparison unplugged. While granted the pinecaster is a pine body and the blacktop is alder which does affect the character of the tone a good deal of what matters in articulation has to do with how the finger greets the string and fret.
Overall I can't tolerate high action strings on any instrument. Low to medium low works fine for me with some caveats playing jazz boxes.
In regards to speed for speed sake a question that rarely comes up in discussion is..What are you willing to sacrifice for speed?
When I was a kid there was a commonly held belief that in order to gain maximum efficiency in speed playing one had to always maintain the lowest possible distance between the fingers and the fretboard. No flying fingers When you lifted your finger off the string it was always only supposed to be as high as to get the finger clear of the string. In order to maximize my playing with this approach I went to lighter gauge strings insanely low action thin necks. Speed and timing were everything, tone, dynamics, articulation were less important. I idolized Al Di Meola. Sheer determination was the answer. I put away all interest in other playing styles or even learning songs or writing songs just to be as fast as humanly possible. It worked...sorta. My friends were enamored by my virtuosity, Players many years my senior would often comment on my blazing technique. But when it came to a jam set everything would always fall apart because the tempos I had mastered were much faster then the tempo's we'd play at. Along the way I also developed some of my own original ideas towards playing. Coming up with tapping ideas I hadn't heard anyone do before. Developing a combination "two finger scale" approach mixed with rakes. The truth was ... just because I hadn't heard or seen these approaches used before my ideas on speed playing techniques didn't mean others hadn't done them before. I just was out of the loop. So drawn into my own world of playing the rest of the world passed me by.
It's funny about the whole "flying fingers" thing. I see very fast players like the late Shawn Lane and jazz guys like Robert Conti Conti has huge lift when he scales...
And yet he plays as natural as it gets even at faster tempo's then shown.
So maybe the path I was on lead to my faster playing or maybe it was my sheer determination which accomplished the level of speed I could play at. In retrospect it's hard to say.
Shawn Lane had some interesting things to say about developing speed as a player which run contrary to popularly held beliefs. Including beliefs that I held dear. In retrospect I get what he's saying about the psychological impact.
Regarding flatwound strings....
I love them. I don't always play with them as they are considerably more expensive then round wounds. I love them for the tone and the feel on my fingers.