Its not about limiting losses its about playing a big pot out of postion.
Sometimes this is unavoidable. Navigating large pots while OOP is never easy, but it's a necessary skill to develop if you want to be a winning NLHE player. Otherwise you need to avoid playing OOP in all but the most opportune times, and quite frankly that isn't reasonable.
Personally, I'm usually sort of relieved when I'm dealt junk in early position. But I'm not folding premiums if that's when they're dealt to me. Sometimes you just need to do the best you can with what you have to work with.
If we bet and he folds we get no value.
Dragging a pot uncontested is a better result than giving a free card to someone who can possible improve to a winning hand. Yeah, it's a bummer when that happens in a situation where you want action, but most of the time, winning a pot regardless of what I'm holding is always a good thing.
No flush draw is folding. Im not worried about protecting our hand as i agree with you we are usually way ahead of his range. We have good show down value and i want to get there with him building the pot.
We don't want the flush draws to fold. We want them to call when we lay them an unprofitable price. Will they get there sometimes? Of course. But this is about which plays have the highest EV in the long run.
Take the hand in question. Say hypothetically Villain folds to HERO's river value bet. He would have put in xx amount of dollars on the previous streets and gotten nothing in return EV-wise. HERO gets max value this way. Conversely, HERO makes a large mistake EV wise by failing to bet his hand. Not only does he earn less money in a pot he was destined to win, but he also laid infinite odds to his opponent by allowing them to draw for free. Both of those are an EV disaster.
HERO was the preflop aggressor in this hand. There's no reason to believe Villain will bet if checked to. Maybe if HERO checks the flop and the turn you could expect the Villain to bet, but this line relies on too many assumptions and has too much downside - the downside being the risk of giving free cards while the Villain also realizes his equity by checking back.
Sure - there's merit to the axiom that it's better to win a small pot than lose a big one. But failing to extract value is one of the worst mistakes a player can make. If you have a chance to stack someone but let them off easy that's far worse than losing when someone's draw got there in an otherwise properly played hand. This is because of the infrequency of such hands.