A recent paper compares measure of "psychological wellbeing" between people whose most recent relationship was casual versus serious, and finds no difference. The paper motivates itself by the speculation in public discourse and the teachings of abstinence-only sex education that casual sex is harmful.
The qualitative research on the subject of casual sex seems pretty clear that, to the extent that they exist, the harms of casual sex would be unlikely to be found on a psychometric measure. Kathleen Bogle's qualitative study found that college-aged women feel frustrated and sometimes their feelings are hurt by differing expectations, which is also consistent with what Laura Sessions-Stepp reports in her journalistic book. I haven't ever seen anyone suggest higher rates of mental illness among people who have casual sex. It seems highly unlikely that casual sex poses a public mental health problem. (Casual sex does likely increase the total lifetime number of sex partners, so increases STD risk, but that's not the main issue here.)
The lack of a quantitative measure for romantic frustration doesn't make it unimportant. Just as quantitative research finds that married men seem to be in better physical and mental health than unmarried, but no difference for women, doesn't diminish the importance of the desire of many unmarried women to be in committed relationships. Likewise, quantitative research finds that people with children are more unhappy than people without, and yet there is an entire medical subfield dedicated to making people unhappy by helping them have children. (Likewise, my understanding is that US medical doctors stopped performing sex reassignment surgery after quantitative studies found no improvement after surgery, and yet qualitatively transgendered people who choose surgery report an improvement.)
Intangibles are important. Keep those qualitative studies coming.