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.
Don’t mind me, just taking advantage of a good Marxist meme to plug my Read Theory, Darn it! introductory reading list on Marxism.
As the contradictions within Capitalism sharpen, more and more workers are radicalized and develop Class Consciousness, but without reading theory, this can be taken advantage of by opportunists. The Capitalist machine is very good at this, they redirect problems with the system itself to other areas, like immigrants, queer people, and more. Theory helps cut through that smokescreen and allows us to see how to move beyond Capitalism.