like chipmixer will try to drain all the available chips, the site will provide new chips, they can monitor who sells it to Chipmixer and they will be able to reach the state or the party that runs the site
No one sells coins to ChipMixer. The chips they distribute are created from consolidated outputs from other users' deposits. For a large entity to "drain all the available chips", as you put it, they would first have to deposit at least as much bitcoin as the total value of all the chips. If they then drained all the available chips, then ChipMixer could simply recreate the same number of chips again from the deposit they received from said entity. There is no one selling coins to ChipMixer and so no one to track or monitor.
Government simply could use service offered by those blockchain forensic companies though. It's more effective (and might be cheaper) than creating their own forensic from nothing.
We already know that dozens of different government departments in the US alone spend tens of millions of dollars on the service of blockchain analysis firms. For example:
https://www.usaspending.gov/keyword_search/chainalysishttps://www.usaspending.gov/keyword_search/ciphertracehttps://www.usaspending.gov/keyword_search/coinbasehttps://www.usaspending.gov/keyword_search/ellipticI cannot find the video, however, Charlie Lee said it would take at least 7 hops before an exchange will not mind where your coins came from anymore.
Pure guesswork, and it highlights just how stupid taint and taint analysis is. Some exchanges might think coins are clean after 3 hops, some might think 7, some might want more. Completely arbitrary nonsense.