Investors should be compensated for accepting systematic risk, as it cannot be diversified.
Why do the investors need to be compensated for accepting systematic risk? Because no one can avoid it and nothing can be done to prevent it. I understand that if not given a suitable return, no investor would accept the systematic risk. But why compensate? And who is going to compensate them?
Your premise is mistaken. You can avoid systematic risk by investing in a risk-free asset or one that has no systematic risk (e.g. under the CAPM, that would be an asset $i$ with $\beta_i=0$). Since investors are typically risk averse and they have the choice of investing risk free, they will take on systematic risk only if they get some extra compensation for that. The compensation comes in terms of positive expected return in excess of the risk-free rate.
