In the early game it can be worth it to give them those open borders, often they offer 1 gold per turn which isn't bad. I usually don't get offers of 1 gold. If you want long term friendships, this is the first step. Usually some turns after you accept their offer of open borders they will propose a declaration of friendship. And eventually you can work up to alliances (assuming you have Rise and Fall expansion). And yes, if you aren't planning on conquering huge amounts, it is very worth it to invest in alliances. The bonuses are quite good. If you are going full on warmonger, then don't bother. Keep in mind though when you accept those kinds of deals, that if you haven't settled everywhere you want to settle, the AI may try to sneak through and settle behind you (though with luck it will loyalty flip), so giving open borders isn't entirely without risk, but worthwhile if you want to try to establish friendships.