Don't halt playing him. Keep playing him in normals if you don't feel like playing him in ranked. He actually is a good champ to play support on and he gets better and better as you learn more things you can do with him and climb to the point where people click on the lantern. That's the thing about thresh, people will always forget about it so you can't let yourself get tilted when they don't. Just release in bronze (particularly lower bronze) you are going to lose a bit of power in his kit because teammates and you have to work that much harder to make up for it.
I know that kind of counterdicts what I said, but that's sort of thresh's biggest issue for most players: people aren't going to click the lantern that much until gold, it gets frustrating, but you also need to keep up your practice on him because he's one of the better ones to know.
Also if you think you are good on him, you really shouldn't give him up. If he clicks for you, keep at it. Just not in ranked if people are tilting you that much.
Morg is pretty good, she's an Annie/zyra type. Taric is a good tank. Leona is fine, but I'd be a little hesitant to play her in bronze only because she falls off very hard in the late game and in bronze, games are more likely to go late. If you pick her up, just understand you are going to need to keep your teams focused on objectives, that you need to win early, and that you can't force a bad trade during laning. Nami is good, but you need to be able to land your Qs on her and make the most of her Ws.