Its not even about him being "the best available".
Lets just take a look at the three guys on the island (we're not counting the visitor).
- The MC. The guy is only there because of his brother getting him a job on the ship. Despite that, he has shown himself to be a resourceful, multi-talented guy, able to think outside of the box, a willingness to admit that he doesn't know something as well as a willingness to learn and to defer to someone who knows more, be it learning engineering or a new language so that he can talk to a girl in her own native language, instead of making her struggle with English. He's also an astute student of human nature. Add to that that what he builds/makes often has a positive psychological effect on the others (did he need to repair the resort pool and build a bar? No. But given that everyone has the basics of food, shelter and water covered, there are other needs to be taken care of).
- Eric. The first thing he does on the island? Brings back capitalism. And that's his biggest contribution.
- Davi. Treats his girlfriend like crap and sulks in his room the rest of the time. Oh and despite being in the construction industry, doesn't help in the restoration of the bridge.
The MC has taken the opportunity to remake himself into a better guy, and the girls notice that. And they appreciate that. A lot. And they tell him, like actually thanking him for all he's done.