R.E. You not being able to host:
Being in CZ does not put you at a disadvantage, your timezone is the same as mine which means you should be able to join many hundreds of players in North or East Europe and experience good (low) ping.

The game does not have a bias for choosing host from certain countries - it uses many other logic which I have not bothered to fully comprehend but I know tricks that allowed me to easily become host when using PCs in several different locations (e.g. NL, DE, UK, DK, SE & LTU)

The easiest way to test your theory is to open your NAT and become host yourself. If others do not complain about bad connection, then likely your connection is not as bad as you suggest.

A Kicktool is designed to allow a player to block another players IP (a temporarily timer is equal to kicking a player out the lobby and a non-expiring timer is considered banning a player from the lobby).

MW2sa was out for 10 years prior to my Kicktool so I assumed everyone knew what a Kicktool is meant to do and how it is meant to work, but in case you want more info on what my tool does and how it should be used, you can read the link below:
https://steamcommunity.com/groups/MW2LT_AdminTool/discussions/0/3115920924812163579/

Using advanced features to migrate a host or close the modded Lobby is not the focus of the program, it's simply a perk. So to say it does not work without having made use of the main functions is a premature judgement.

I haven't tried to host the lobby myself - Czech Republic may be in the middle of Central Europe, but the other states alike Russian Federation would have some huge ping, as it's quite a distance from there to there.

Renaming wasn't present.
In the cases I've reported, I've tried to kick the host outta his lobby - The hosts were, indeed, cheaters with wall hacks or aimbots.
As for the last question, I can't really answer that, as I do no longer remember that.

Have you hosted lobbies yourself?

A cheater or "hacker" cannot stop themselves being kicked, they can only distract or fool the host with their tools in such a way to result in them not being kicked

E,g, a cheater might rename to another player nickname while the match is in-progress so you no longer recognise them in a list? (Just an example, not a working scanario)

However, you've not once reported such an occurence to me even once, so I wonder when you say: "the kicktool simply „doesn't work“ on them" - what you are basing this on?

I've been using the MW2 kicktool for a while, but.. From what I've observed and experienced so far, those cheaters, sometimes even hackers, do know, how to stop getting kicked from their lobbies, so the kicktool simply „doesn't work“ on them.