Capitalism without inequality is contrary to its definition

I mean kinda, but it's a matter of degrees. Capitalism revolves around the private ownership of capital, so will not enforce a given level of (in)equality. Still though, the overall amount of inequality (I.e. by the GINI index) can vary quite dramatically between capitalist societies. From Brazil up in the 60's to Germany down in the 30's.

I don't know but if people could agree to take just a tiny bit of profit, everyone would be happy. Sure, inequality would still exist but it wouldn't be the-top-one-percent-owns-half-of-the-total-wealth inequal

I mean not really. Certainly could be argued that it's the natural conclusion of capitalism in our society, but it's not the point. With capitalism as intended, the worker who is working longer hours in a position far more crucial to society should be earning significantly more than the fat cat who is making little positive impact on society and is working shorter hours.

So yeah, pretty much any real-world implementation of capitalism will reach this result because greed exists, but the ideals of capitalism are quite opposite.