I've not yet played many games with civs with great people, but Greece is an exception. I have a tendency to dig into one civ until I've figured it out. My verdict so far is Logios are terrible. As you pointed out, the bonuses they give are neither permanent nor significant, and some of them provide bonuses to late-game buildings like Academy and Amphitheater. What am I supposed to do with Aristotle when I'm at least 30 turns away from getting my first Academy? The only Logios that I've found worth getting is Thales. In one of my games, I got 10 science from him, although I couldn't figure out exactly how because I don't think my city was generating 20 influence per turn. Logios just don't work out because they're just not worth the production early game, but the later you get them, the less value they provide. Honestly, they're at best as useful as Ancient Walls, which I'd often rather get at the end of Antiquity in case my neighbours decide to attack at the beginning of Exploration.