rowrowEither way, you'd think there'd be an easy way to solve the issue of hackers with the vote system keeping track of their votekicks and notifying someone or something about it.
There is no easy way of "solving the issue with hackers". Any solution that actually solves the problem would be extremely complex and would require basically invading privacy and consumer choice on a level not really seen in any other entertainment market. (e.g. forcing people onto specific systems that monitor literally everything you do ever on them) Considering the massive shit storm Valve received when VAC checked DNS history for a very short time, this is pretty much never going to happen. Even in games where pretty much all important information is server sided (which to keep this short this isn't very easy to do in an FPS), people still cheat with stuff like macros. Cheating is a war that no one realistically can win against, just massively slow it down.
Even if your idea was a good one (and I'd argue it really isn't, I got votekicked on Valve pubs before for being a "cheater" and I'm not even that good at this game mechanically, just being decidedly mediocre at DM from a competitive standpoint is still being a god in Valve pubs, and comp MM isn't much better), it still wouldn't ban anyone instantly because not banning instantly harms hackers more than banning instantly benefits players. The only time VAC instantly bans is if it detects a hack that has been VAC detected for a very long time (like years).
Now looking at your original post, that's just not how VAC works. Valve employees have very little to do with VAC. Employees only real interaction with VAC is adding signatures of cheats to the ban list and reviewing code of anomalies that VAC uploads to their engineers to see if it's a cheat or not.
VAC also doesn't "need a break" to check anyone out, any time you're on a VAC enabled server it is checking you out. The tl;dr simplified way of how it works is every account is assigned a "Challenge Level", and then when you connect to a server you download a specific piece of VAC3 related to your Challenge Level which gives your client a challenge. If your client fails the challenge it is considered an anomaly, will upload that data to Valve for them to determine if cheating is going on via the code it uploads of what triggers the anomaly and cross references it with their already existing cheat list, and then your Challenge Level is increased and it will do increasingly more thorough challenges. If you are determined to be a cheater you are flagged and then banned an indeterminate time afterwards whenever Valve feels like it basically. This is on top of a heuristics RAM/process scan that is always on-going that attempts to detect an anomaly that way to send to Valve and can increase your Challenge Level further. In fact, banning someone like this would actually prevent VAC from checking them out with harder challenges or trying to figure out what they are running (although it is most likely something not detected yet since there's still plenty of private cheats better than lmaobox floating around), since you need to be connected to VAC for it to check you out, which only happens when you're on a VAC Secure server in TF2.
So your suggestion would actually be counter-productive and result in them getting detected less because it's preventing VAC from even searching them and Valve doesn't do manual checks.