Beta as risk measure for diversified portfolios

Why is beta, as opposed to stdv., the appropirate risk measure for adding additional securities for well diversified portfolios?

Beta measures systematic risk , which is the market risk that is left when company or industry specific risk is diversified away. In a well-diversified portfolio, there should mainly be systematic risk only, which is what “the market rewards”.

Stdev measure total risk, of which systematic risk is a subset.

Therefore, when looking at a well-diversified portfolio with only systematic risk, Beta is the correct measure.

On the other hand, if a portfolio is not well diversified and has a lot of idosyncratic, unsystematic risk, stdev is the appropriate measure of total risk.

Got it thx a lot!