Can Minion damage matter

They matter more in the early game and less in the late, even if they've increased their damage; it isn't substantial enough that a champion notices past 35 minutes because they only do physical damage and most champs have a decent amount of armor by then and/or life steal.

And as for top lane, the minions matter plenty early game because they hit like a truck. What, do you want them to two shot people? Standing in a wave of six minions letting them hit you pre 5 minutes is still going to hurt no matter where you are. .-.

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Given their name, likely top lane where other than cannons, minions don't matter at all. Also, in contrast to your point, they were changed to actually increase their damage as time goes on, to the point that 35 minutes in, they hit over 6 times as hard as at the game's start.

Minion damage scaling only effects forcing the game to end, like Baron buff and taking Towers and INHIB so it's not just a stalemate. Can't really ever say mid-late minions did anything worth noting to champion fights in s9 though, only early laning.