Does Segwit mean easier government monitoring?
No, that's completely wrong. There is absolutely no anonymity benefit to third-party transaction malleability.

Third-party transaction malleability makes use of a symmetry in ECDSA signatures that allows changing a transaction's id to exactly one alternative id. The alternative signature has been deprecated and non-standard for years, but miners could still confirm a malleated transaction if they chose so. In fact, it's rather simple to convert transactions from one txid to the alternative txid, and this happened recently, when Bitclub mined a few malleated transactions. Besides a few poorly coded websites suffering hiccups, this was largely a non-issue. However, this issue currently delays use-cases that rely on chains of unconfirmed transactions which would be broken by a malleated transaction in the middle of the chain being confirmed. 

Transaction malleability is completely irrelevant for tracking, because tracking typically happens after the transaction is confirmed and therefore has already become immutable. Since the connection is made via following from transaction outputs to outputs, there is no hindrance whatsoever due to a malleated transaction.