This criticism of democracy is way older than Kennedy. Socrates thought democracy impossible due to the ignorance of the common person.
And that's what this is, an argument against democracy. A vote cast by a shut-in illiterate who chooses candidates based on their astrology sign is just as valid as the chair of the political science department. Anything less than that is an argument for weighted or exclusive suffrage. You can believe in democracy or the "low information" voter, but not both.
Acknowledging that democracy as glorified sortition is not actually in any way better than sortition is not an argument against democracy; it is an argument for creating the circumstances in which an active citizenry meaningfully and knowledgeably participates in the civic life of their polity. It's not about 'weighting' or making suffrage exclusive, it's about creating a society in which good citizenship is enabled and valued by the institutions of society.