From Jack Mountjoy, forthcoming in the QJE:

This paper studies the returns to enrolling in American public universities by comparing the long-term outcomes of barely admitted versus barely rejected applicants. I use administrative admission records spanning all 35 public universities in Texas, which collectively enroll 10 percent of all American public university students, to systematically identify and employ decentralized cutoffs in SAT/ACT scores that generate discontinuities in admission and enrollment. The typical marginally admitted student gains an additional year of education in the four-year sector, becomes 12 percentage points more likely to ever earn a bachelor’s degree, and eventually earns 8 percent more than their marginally rejected but otherwise identical counterpart. Marginally admitted students pay no additional tuition costs thanks to offsetting grant aid; cost-benefit calculations show internal rates of return of 26 percent for the marginal students themselves, 16 percent for society (which must pay for the additional education), and 7 percent for the government budget. Earnings gains are similar across admitting institutions of varying selectivity, but smaller for students from low-income families, who spend more time enrolled but complete fewer degrees and major in less lucrative fields. Finally, I develop a method to separately identify effects for students on the extensive margin of attending any university versus those on the margin of attending a more selective one, revealing larger effects on the extensive margin.

That is one simple way of seeing why I do not think of higher education as largely signaling, noting that signaling theories might give you a higher wage up front but not over extended periods of time, as worker quality becomes known.