It is correct some things that you say, however, I differ in some things. And these are the reasons:
Not everyone who has it knows 100% of what the program is about (since they may download it for something specific, without knowing all the other functions that the program has). A high percentage of users don't know how to block certain options, so when installed, if you have not known how to modify the configuration you will be giving total control of your computer to a stranger.
In fact yes, it can be used with some of the computers turned off. For example, in the case of TeamViewer, in its package it brings the function of "Wake-on-LAN (WOL)" What is it? a function that can turn on a computer off or in sleep mode. BUT, this function is not allowed by a MAC computer that is completely turned off because Apple doesn't allow it, but in sleep mode it does.
We hope to avoid that this "50%" doesn't increase, more rightly, these warnings should be applied. Before the programs becomes more recognized and innocent people who don't know about it, begin to fall into their downloads through cheating and scams. (Regardless of who asks to download them).
There are too many ways, with advanced coding, complicated programs, viruses that drop on your pc to collect information including cookies, saved passwords, open sessions, and get it on their linked server, etc. Something that can also be done in a simple program like Skype. The safest of all, is never to click on any link, or accept unknown files, however the other warnings can be useful information to reinforce knowledge.
Keep in mind that I didn't name all the programs, I relied more on "TeamViewer" however, the other programs are very similar to this, and have almost the same features and functions, but for obvious reasons I can't explain one by one. It is something general that includes several programs. (Those two are the most recognized so far). In this case, the rest is obvious.