The downside of Bitcoin and Ethereum is that on-chain scaling is just not a viable option moving forward, especially with the number of transactions they already generate on a daily basis, hence the reason that both are working towards a future where second layers will be where most of the transactional activity will take place.
If we're talking about scalable blockchains/networks within crypto, then EOS pops up, TRON, XRP. They have already shown that the speed and cost of transacting is not a problem, mainly because they don't aim to be decentralized. Not being decentralized grants you the freedom to scale into oblivion, and that's what these networks will do if the demand asks for it.
Goverments will most likely follow the governance model of EOS and tweak certain aspects for even more control.
Exactly. Centralized blockchains are more scalable than decentralized ones because of the way they're designed. Most of these blockchains don't depend on miners to work as intended (like XRP, XLM, and even IOTA). By eliminating miners, you could experience an upsurge in transaction performance. Also, the short block times greatly contributes towards higher transaction capacity. It's the perfect model for worldwide governments to adopt for their own digital currencies. This all a matter of sacrificing decentralization in exchange for higher transaction throughput. A cryptocurrency can be extremely secure but terribly slow in transaction processing time (like Bitcoin). On the other hand, a cryptocurrency could be lightning fast but highly insecure (like it's the case with most DAG-based cryptos like IOTA and NANO).
Despite these facts, governments will make use of a Blockchain network that will prove to be the most efficient one for them. One of the best candidates for this is EOS, due to its asynchronous scalability design with a fee-less structure. Governments could easily fork the EOS blockchain to create one of their own. Whenever this will boost our economy or not it's yet to be seen, as Blockchain technology is still in its infancy. I'm afraid that our economy will remain the same, as governments maintain the inflationary supply of their Fiat currencies.
Nonetheless, it's no secret that governments will adopt Blockchain technology for their own benefit. As they test different solutions, they'll launch their own digital currencies for the mainstream world to use. After all, our economy will improve or remain the same depending on the measures governments take for their national currencies. If they decide to charge little to no fees for each transaction, then it could bring greater demand causing our economy to gain traction like never before. But if they don't, then our economy will remain likely the same with the only difference that everything will be transacted within the digital world instead of the physical one. Just my opinion