Why does only systematic risk exposure matter for the risk premium, i. e., how does the price adjust to make only systematic risk affect the expected risk premium

Because it can be mitigated through hedging or by using the correct asset allotment technique, unlike unsystematic risk that can be diversified away.

Explanation:

Systematic risk is a term in finance and economics that describes the available risk to the whole market or portion of the market.  

Also, given that, systematic risk is sometimes referred to as “undiversifiable risk,” which concerns the all-around market, and it is considered to be unpredictable and impossible to completely avert.

Hence, only systematic risk exposure matter for the risk premium because it can be mitigated through hedging or by using the correct asset allotment technique, unlike unsystematic risk that can be diversified away.

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