[Saxon]

While the enemy has "your" provinces and is searching for special sites, they are getting income from them. I would rather deny them the income and have it myself, even if that means I do not get as many gems later.

All else being equal, the person with the most income (of all types) will win this game. The earlier the income advantage begins, the sooner they can use it against you. I would not want to give that advantage to another.

Of course, things are never equal in this game, but I would still need a very, very good reason to give up the income.

Further, what if the enemy takes "your" provinces and never searches them for gem sites? You take the province back and get nothing special. You still lose the income and get nothing for your risk.

In short, I would focus on improving your early game strategy and tactics rather than risking this strategy.