Finding NPCs is always difficult on patch day. You can improve this by:
  • Typing /sconfig, going to Other Settings and reducing Character and Object Quantity to Minimum.
  • Holding X so that only quest things are clickable. Note that this may not have this effect if you altered the click filter settings.
You also have the option to visit other instances, worlds or data centers with less congestion.

As for zones reaching their cap so that nobody else can enter, I have only seen this once and it was when Asmongold started streaming the game. Limsa Lominsa Lower Decks actually reached its overall cap so he could not leave the tutorial area. That's extraordinary, because when EW released, instances had over 500-600 people in for Chi. It took a person with literally 200,000 viewers to achieve congeston even worse than Chi. In a situation like his, it could help to have a private instance that can be requested, but it's pretty niche for a streamer to be that big and he could have started on a less congested DC at the time.

For the most disruptive players, a streamer can report them and in 7.0 they will be able to blacklist them so they don't render.