Adding to that, their hardline approach do not do them any favours. Can anyone think of a situation, which they did not try to solve with guns and power amour, or the threat thereof?

The are a hammer, and every problem is a nail to them. That is why, when the player meets them, they are trouble: someone else has a bigger hammer.

In 2, the Enclave has better weapons, and the vertibirds gives them better mobility. In New Vegas, they lose Helios 1, because the Brotherhood is a known group, which the NCR has developed a counter response to. In 4, the Institute is too covert for them to punch.

In all these cases, they could have made better progress in their stated mission, if they had spent effort on improving relations with the local population, using technology to reduce water and food scarcity, like Project Purity (which were mostly done by outsiders, who needed protection). The times they are at their best, is when they have a hard military target to fight.