That's not what Socialism is, or even Communism. In every existing Socialist state, people have gotten higher or lower pay for different levels of intensity or skill. If getting paid the same is "the problem with pure socialism" then it sounds like it's all cleared up!

Secondly, Social Democracy still relies on Capitalism, which necessarily moves in the direction of increased disparity and centralization of power in fewer and fewer hands. Moreover, as companies spread internationally, Capitalism turns to Imperialism, whereby workers in the Global South are paid a fraction of the wages a worker in the Global North would be paid. This form of hyper-exploitation for super-profits results in dramatically unequal exchange and underdevelopment. Socialism is the way forward, beyond this system of exploitation and eventual collapse.

I really recommend you give at least the first section of my reading list a try.