It's one of ideas that are interesting/fun to discuss, but unlikely to be used by average people/miner. From miner side, they need to use wallet that support Silent Payment and patient enough for longer sync time.
I don't think you still need to hide your mine BTC since it was fresh from the solved block and transaction fees.
However, if you care about your privacy because I know some pools were being hacked and leaked most of the personal data, including miners' earnings, this silent payment will give you no privacy leaks compared to using the standard one.
The author mention this as mitigation.
Compromise of the mining pool database is likely the largest threat vector to privacy for those paid. Ideally, the pool only retains share accounting data for a duration necessary to calculate and payout hashrate providers then nukes the accounting data, helping secure the privacy of past blocks.
But i doubt there's demand for mining pool that minimize data collection/retention.