I want to expand on @raghav’s answer a bit (which is great! I agree with what he’s written), as I’ve thought about this before as well.
I see two options for getting these transactions mined: pay a miner to provide this service, or mine them yourself (solo mining, or become a pool operator).
Additionally, there are then two approaches you could use to launder the funds: conspicuously, or inconspicuously. The distinction is not absolute, but it basically comes down to ”does this transaction stand out from the ‘average transaction’, in terms of fees?”
First off, no matter how the transaction is mined, if the fees are conspicuous then you have not added sufficient obfuscation to the flow of funds to have truly broken the trail of audibility for anyone performing an informed investigation. So this method seems to fail, in any case. We can ignore it, regardless of whether you are mining your own blocks, or not.
So then, we can explore the two remaining options: mined by a third party with inconspicuous fee rates, or self-mined with inconspicuous fee rates.
If you are paying a miner to perform this service for you, then rationally you should expect to pay: the going fee rate, plus a service charge for the added overhead of the service provided. So already, you will need to pay a slightly higher fee than is otherwise required to confirm a transaction, and you have not actually laundered any coins yet.
So this begs the question: how much can you add in ‘extra fees’, before the transaction becomes conspicuous? Perhaps double the fee-rate would be acceptable, but in this case you will effectively be paying ~50% in order to launder funds, and this seems quite expensive at first glance. For large amounts of BTC, even double the fee rate does not amount to much throughout, and looking at recent blocks (height~566,527 at the time of writing), we can see that the total fees for the average block are consistently below 0.5 BTC (most seem to be in the ~0.1-0.3 BTC range). So even if a miner stuffed a block entirely full of your transactions (which may be conspicuous in itself, depending on the relationship of addresses you use to fund transactions), you’d be looking at laundering maybe ~0.5 BTC at most per block. In the future, fee rates may change, but in all but the most extreme cases this seems to be rather inefficient.
Additionally worth mentioning: the miner providing this service could keep record of the transactions, so you would have to place some trust in them to keep this information strictly confidential. Also, you would have to trust them to pay the coins out to you as specified.
So what about the option of mining the transactions yourself? In this case, it is worth noting that you will no longer have to pay the ‘service fee’, but I don’t think you can fully discount paying the ‘usual fee’ that a miner would otherwise expect to confirm your transaction. This is because not receiving the miner’s fee is an opportunity cost that you will pay in order to mine your own transactions, and since mining is highly competitive, forgoing the collection of these fees may affect your return on investment for the mining operation. Of course, your ‘profits’ will come otherwise in the form of laundered BTC, but I thought this was worth mentioning nonetheless, as you will otherwise be ‘less profitable’ than other miners, all else equal.
So the question then becomes: is the investment risk of a mining operation that is large enough to reliably solo-mine blocks worth it? Or does some other method of laundering BTC incur less risk? Or more reliability?
Keep in mind, even with your own mining operation, you still have to keep transactions inconspicuous, so as mentioned above, you would be laundering just a fraction of a coin per block. In order to launder a significant amount of BTC, you’d need to find a good number of blocks, meaning a larger investment in mining equipment.
I think the TL;DR is thus: given the high costs and risks of laundering BTC through coinbase transactions, there are likely alternative methods that are more efficient and effective. This conclusion is perhaps premised on low fee rates (sat/vbyte), but even with high fee rates we see that paying a miner to perform this service will be expensive (a high portion of your coins paid as fees), whereas running your own mining operation requires a large amount of upfront investment/risk.