Indeed two very different approaches can be taken by classic banking institutions: one is to embrace&conquer, and the other is to adopt. It is technically for classic banks to take the first with a long term goal, as you said, to enter the market for the purpose of controlling it from the inside; however, the decentralized nature of crypto makes this very difficult, to the point of being inconvenient. Banks will only do what suits their bottom line, and it would take more than an isolated effort to have any significant control (not to mention crypto can always redefine itself with a new unbiased token).