downvotes are redundant

In practice they are redundant because most people vote based on opinion, so both become the same (agreement gauge). However ideally they aren't redundant; upvotes are to be given to things that stand out, and downvotes to things that detract from the discussion (noise, trolling, etc.)

Those that downvote willy nilly just want to have more say in things than others who don’t have energy to religiously clean website from „wrong” content.

Some see this as an abuse of the system, not as its normal usage. I'm not sure on the dividing line between both things, though.

If you [=anyone] don’t like what’s being said but it doesn’t break rules then reply and explain why is it wrong, let others upvote if they agree.

The problem with that is Brandolini's Law: even if we ignore "intention" (whatever this means), it takes far more effort to address bullshit, assumptions, oversimplifications, "ur sayin dat cuz ur..." etc. than to come up with it. And if it takes too much effort, people won't do it.

As such, a system can't rely solely on replies to let users show each other "hey, this post/comment is bad".

You can rely on stricter moderation; but that comes with additional costs.

Tildes solved this already.

Incidentally my proposal to fix downvotes isn't too different in spirit from what Tildes do.

So, people want to up/downvote based on opinion, right? Let them do it. But give people other ways to quickly show some piece of content is bad, and why. Effectively splitting the downvote button.