Carruthers’ video is great for explaining what a luthier should do to get a bass into factory spec.
The problem is, I don’t want my bass in factory spec. I want it set up so it feels right to me. For me, I like a much lower action and a bit less neck relief than factory spec. So even if I DID use a feeler gauge, it would not be the final adjustment anyway. To me the feeler gauges are pointless and I lose nothing by not using them.
Nut height is something that is nice to tune but is not going to cause much issue unless it is way out of wack. I have filed mine once though (when converting a bass to BEAD) and it’s not very hard, just not strictly necessary. I will say that Warwick wins the game here though; having an allen-adjustable nut as a standard feature is super cool.
Any tuner will work for intonation, it doesn’t need to be a strobe.