Where the "three mistakes" pattern comes from
It's borrowed wholesale from mobile match-three games, where a life system is the entire monetisation model — run out, wait or pay. Sudoku doesn't need it. A wrong digit in a logic puzzle is just information: you tried something, it didn't fit, you try again. Capping that at three attempts before the app interrupts you isn't protecting the puzzle's integrity, it's manufacturing a moment to show you an ad or ask for a subscription.
The same thing happens to hints. Revealing one correct cell costs the app nothing — it already generated the full solution to build the puzzle. Charging coins for it, coins you get by watching 30-second ads, is a business layer stacked on a feature that could just be a button.