Nexus turrets should deal splash damage.
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Nexus turrets need to do a shit ton more than that. The only reason they keep defenses so weak is to give teams way behind a chance to outplay the winning team hard and push to win. They don't want a losing team to get a huge pick and ace and then not be able to take advantage and win the game. I can see that logic but still I think it's unfair late game or any time really.
I don't think they should do "more damage" per say...But I think they should scale better into late game. I find it kind of stupid that any given tank can just soak several turrets with his team, taking away the need to keep your minions pushed at lvl 18.