We dont gain equity, our fold equity doesn't really improve a ton, the 7 isn't a scare card, he wont put us on trips, a K is never folding. And like in the example he isn't guaranteed to fold all pocket pairs.
It looks like a spot where if you're going to fire the turn you should fire all rivers too to increase the chances he folds all these pocket pairs but it depends on how often he folds to c-bets, player type etc. No point getting sticky firing 3 here if people dont like to fold much, which they dont at 4nl. If he folds to 60% of c-bets anyways it's probably more likely he has hit a tp and then firing 3 is just suicidal, so yeah depends on a few factors, but just firing the turn isn't really great for us.