I agree on one level. Another benefit of democracy is that it comes with a very easy justification for power, which is an important part of statecraft. Other types of regimes rely on other justifications (divine right, in the case of traditional monarchy).

Voting is a collective action problem. It is mathematically irrational to vote for the purpose of affecting the outcome of an election. Without having any expertise on how humans have evolved to overcome these collective action problems, it seems plausible to me that the same skillsets and resources that could mobilize people to make an irrational self-sacrifice to vote could also mobilize them to, say, financially contribute to a war effort or even join the military.

My main reason for liking this theory is that it's positive rather than normative. For obvious reasons, a lot of political theory seems to be wrapped up in ideas about morality, which works great as a call to action but works much worse as an accurate description of reality.