There’s nuance that you’re not including. VAC and game bans are dependent on a per game basis, and don’t apply to ALL multi-player servers, just “VAC secured servers” (which makes sense if you got banned by Valve Anti-Cheat), with the sole exception being Valve games that utilize the same underlying engine for their multi-player (CS:Source and TF2, GoldSrc games, so on…) with the same restrictions.
You can still play VAC and other anti-cheat supported multi-player with games not related to your ban, but you will still have VAC bans on record on your profile, which people may cite to kick you.
All of this (apart from the social stigma) is plainly documented on Steam Support:
There’s nuance that you’re not including. VAC and game bans are dependent on a per game basis, and don’t apply to ALL multi-player servers, just “VAC secured servers” (which makes sense if you got banned by Valve Anti-Cheat), with the sole exception being Valve games that utilize the same underlying engine for their multi-player (CS:Source and TF2, GoldSrc games, so on…) with the same restrictions.
You can still play VAC and other anti-cheat supported multi-player with games not related to your ban, but you will still have VAC bans on record on your profile, which people may cite to kick you.
All of this (apart from the social stigma) is plainly documented on Steam Support:
https://help.steampowered.com/en/faqs/view/571A-97DA-70E9-FF74
https://help.steampowered.com/en/faqs/view/647C-5CC1-7EA9-3C29