"Virgin bitcoins" is a thing, but not because of privacy - some investors want them because it gives them a guarantee that there's nothing shady in their coin's history that might lead to attention from officials in the future.
Without a doubt, it's extremely difficult to solo-mine blocks on the Bitcoin blockchain. But in the case of altcoins with low network hashrate, that's another story. It's true that mining equipment sales are monitored "across borders", especially when it comes to ASICs for mining Bitcoin. But there's always the choice to "rent hashrate" in order to divert the attention from the government. Coins like Ethereum and Zcash are mineable with GPUs, which allows miners to have a greater level of discretion. Sending GPUs across borders will not raise suspicion, unlike ASICs. One could easily justify that those GPUs will be used for gaming. Then, miners can exchange their mined altcoins to BTC using a non-custodial exchange to avoid exposing their identity to the authorities. There are many ways to do this limited to one's imagination.
It's a good thing that "newly-minted" Bitcoins have no previous inputs. If miners decides to leave those coins on the Blockchain without moving them, no one will be able to link those coins to their identities. Personally, I would mine Bitcoin on several addresses without moving them at all. If I'd want to sell them, I'd do so via a decentralized exchange. The only issue is pooled mining. Luckily, developers are working on solutions to further decentralize Bitcoin's PoW consensus. If successfully implemented, mining pools' dominance within the BTC network will be greatly reduced. Individual miners will have more power, further increasing privacy and decentralization of the entire Bitcoin blockchain. By all means, "newly-minted" coins are clean (not tainted), making them ideal for mixing services (mixers) in the crypto/Blockchain space. Just my thoughts