(they have to convert it back to fiat in order to spend it is an incorrect assumption, increasingly so even in the US)

They transfer it to someone else/currency exchange location (if not totally banned) and get cash when they need to purchase something, or directly barter with crypto. You don't always need to exchange it with fiat. In such environments, often crypto payment would be superior to cash. (BTW this is not unique to crypto. People could utilize USD/EUR in countries with crappy currencies.)

- can't the government impose whatever rules they want at that step, like the US government does?

I suppose no one does something illegal ever. /s

This is the thing that is hard to comprehend for people in countries where "following the law" is somehow considered absolutely moral and also a reasonable burden. There are jurisdictions that you cannot survive without breaking some law every second. Using VPN to circumvent internet censorship is also illegal in countries with such conduct but regular people do that anyway.

- how is crypto better than gold or equities for this purpose?

Gold and equities, and most importantly land used to partially serve those purposes, depending on the jurisdiction. Crypto is an alternative with pros and cons. The major pro is difficulty of confiscation and ease of transfer across borders if the country destabilizes and you want to immigrate. It helps with geopolitical diversification of assets.