Why would governments want to promote uptake of decentralized currencies in the first place?

Western countries have no interest in Bitcoin directly.

There is an interest to prevent fake medical drugs from being sold. I could imagine laws that force every sold drug to have a verifiable chain of ownership from the factory that produces the drug to the pharmacy that sells it. A chain that's backed up by the blockchain.

In developing countries it can be useful to be able to verify how money travels through the system. Stellar and Ripple provide technologies that enable that. I can imagine a government deciding to pay every of it's employees via Stellar to prevent a boss from taking part of the paycheck from his underlings. Taking tax payments via the Stellar network would further make it the default system.

A government cares about a bunch of long-term predictions about how it's economy is going. It might be worth for creating subventioned prediction markets in Augur for climate changes 10 years from now or for various economic forecasts for which it's good to have reliable data. Subventioned prediction markets might work better than paying government burocrats to do forecasts in many cases.