it’s impossible to have “fair compensation” without uprooting commodity production, doing away with money completely and instead producing things to fulfill everyone’s needs. Only then can things truly be “fair”.
That's Communism, not socialism. Sure, socialism has some similarities to Capitalism, that's because Socialism was never the end goal, but a transition period between Capitalism and Communism.
workers have to exploit themselves by reducing their wages
Workers don't 'exploit' themselves, workers decide if it's worth doing the work for what they can reasonably expect in return or not. If they decide it is worth it, it's something they chose for themselves, not even close to the same thing as a Capitalist squeezing every last cent of 'profit' from you as they possibly can and basically forcing you to do it by making it impossible to survive if you don't.
A person under this system also can’t make full value of their labor, simply because there’s taxes that are used to fund public sectors such as education, healthcare, etc (it’s necessary though).
They still get the full value of their labor. Taxes used to benefit the community benefit workers as well, because they are members of the commuity. Capitalists under capitalism still (are supposed to) pay taxes- and so do workers. Workers who are more fairly compensated for their work and have to pay taxes are better off than a wage slave who isn't fairly compensated and still has to pay taxes.
That is the comparison to make, is Socialism better than Capitalism? Yes. Is Communism better than Socialism? Yes. It makes little sense to tell workers trapped in a Capitalistic system that Socialism isn't good because it's not as good as Communism.
People also are different, some can work more intensely with higher tempo due to how they’re built, and others might not be able to put in the same amount of labor
That's exactly why you don't try and be little capitalists. You can and should still care for people who are in that situation. Workers who receive a more fair share of their labor will be better equipped to help out the members of the community who are less fortunate than them, not less.
it doesn’t abolish capital
No, and it's not supposed to. It just transfers it to the people and takes it out of the hands of the ruling class. "Capital" in an of itself isn't a bad thing, It's when Capital exclusively owned by a small ruling class and used to exploit and siphon wealth from the working class (Capitalism) that's when it becomes a problem.