I don't see why parallel construction would be necessary in the case of bitcoin. Investigators can legally subpoena the records of bitcoin payment gateways/exchanges (that's the entire point of KYC procedures) and then easily link bank records to wallet addresses on the public ledger without violating any laws. It's also a well known fact that this is already possible (hence the creation of tumblers etc), so it's not as if the government would hesitate to do this for fear that the technique would be compromised.

It's not about violating laws. It's about not letting the enemy know when you've cracked their system. If bitcoin was setup (or is just being conveniently used) by a three letter, they will use parallel construction to avoid letting the public know their true capabilities. Popularity of bitcoin would plummet if that capabilty was known.

> they will use parallel construction to avoid letting the public know their true capabilities.

As I already stated, parallel construction is completely unnecessary since everyone is already aware that the blockchain is a comprehensive public record of all bitcoin transactions. What secret technique could the government have that could give them more information than is already available for everyone to see? There isn't any more information beyond what's inside the ledger except for the link between wallet and bank account which everyone knows the government is capable of establishing.

It's not about a secret technique. It's about whether or not they are in fact using the blockchain for this purpose. That little detail is presently unknown by the public, regardless if "everyone knows" they should be capable. If they do not wish to confirm this in public then parallel construction will be necessary to maintain that unknowing.