People not playing the gamemode is not something new in PTP, it has always existed. Back when I started playing, a lot of the regulars would be civ and would be camping at armour. Other times, they stopped being friends and fought each other at armour being cops and terros. Back then, there were a lot more players, so even with a lot of people not playing the gamemode, it would have a minimal impact on the game, as there will still enough people playing it. Now, there's a lot less players in general, so the impact of a couple of people not playing the gamemode is a lot bigger than it used to be, and the effect is a lot more noticeable.
We have taken measures to encourage people to play the gamemode, like changing the scoring system. I'm not really a fan of limiting or forcing people to play the gamemode, because I think that will drive people away from the server. Some people might say that's a good thing, why even have these people if they don't contribute anything to the gamemode:
Sure, maybe regulars who totally refuse to play the gamemode would leave. Who, out of the people who actually play, gives a shit? It won't matter to the gamemode. As it is, there might be 16 people in the server and maybe five are actually playing the GM while the rest are dueling or armor fighting. In terms of the gamemode, it doesn't matter if the remaining 11 leave. The same five people will still be playing.
And I completely understand that point. But you also have to consider the ability to attract players. Players are a lot more likely to join a server that has 16 players, than one that has 5 players. So, in the first case, it will be a lot easier to go to 20 people, and having 4 additional people. With only 5 players, we'll struggle to get to 10 players. So, I don't think it's a good idea to just take measures that will drive those people away, instead we should encourage them to play the gamemode.
As for the ideas, I don't think making terrorists lose health is a good idea. Sometimes, they just don't get to the president, or have other strategies that require them to go to another side of the map first. So, punishing them by making them lose health, will discourage some of the more creative strategies, and I think would negatively impact the gamemode.
Turning off the nametags is an interesting idea. I don't think we should make it like this by default, but we could give people the option to turn off their nametags (to avoid people hunting them, for example). For skins people can do that already (picking a default skin instead of a custom one).