Addressing points, reframing as questions (trying to preserve your meaning), sequencing by specificity and nonambiguity:
Q: Was a time when the majority of the population were college educated?
A: With the absolute peak being both now below 50%, as a strict mathematical statement: No.
Q: When did realistic access to college education peak?
A: The confluence of factors in the 1960--1985 period ... arguably approaches this. Access was not gated by cost, gender, geography, or within a fair approximation, race, but by aptitude and interest. Not perfectly, but better than at any period before or since. The 1977 local maximum (as percent of population) supports this. Present access seems more push-based (obligation/necessity) than pull-based (interest, aptitude), compared to 1960--1980, by rough sense. The BATNA (best alternative to negotiated agreement) to "attend college" was far more appealing then as to now. How to measure this? Hard to say, though the "college premium" or noncollege average or, say, 10%ile annual income, might be proxies.
Q: In the years 1945-85 you would have higher number of people who never went to high school?
A: That's shifting the question from (as I interpreted it) "when the majority of normatively college-aged persons (say, 16--29) had access to bachellors-level education", to "when the majority of voting-eligible residents had a 4-year college degree". The 2nd is a restatement of the first question above, the answer is still "no".
Either way, if you want to translate peak educational achievement to total voting population, you'd have to shift numbers foreward by life expectancy. Say, by 65 years assuming educational completion by age 25 on average. So the US are presently bounded by the 1955 educational cohort, with both secondary and postsecondary attainment growing for the next 22 years to the 1977 maxima. Net of immigration's effect on numbers. By that argument, voter education levels will probably increase for another two decades, though college-level degrees will remain a minority.
This also highlights an issue with the data we're discussing, which measures total poulation educational attainment, and not education-aged attainment. That is, 80% population high-school graduation implies a higher graduation (or GED) rate by, say, age 19. So we're on the hunt for data actually answering our question. NCES does give diplomas conferred somewhere, these can be compared to cohort population with some finagling.
Understanding questions, data, and baselines is critical.
See, e.g., https://www.census.gov/newsroom/press-releases/2017/educatio...
You might like this plot: https://www.census.gov/library/visualizations/2017/comm/amer...
Public High School Graduation Rates
(Last Updated: May 2020)
https://nces.ed.gov/programs/coe/indicator_coi.asp
Gives Adjusted cohort graduation (ACGR), the term you probably want. The racial divides are ... sobering. And not necessarily as expected.)
Q: Is education received as high-quality?
A: This is the tough one. Quality here needs to be considered as "fitness to purpose", and ... well, purpose has changed. There's also the credentialing role of education, and the more credentials you hand out, the
less distinguishing they are, though by inversion, the more arbitrary earlier credentials may have been. High school graduation rates in the US in 1900 were, I forget if it was 6% or 10%, but low. Overwhelmingly male and white, so among that cohort, closer to 25%. (Much attainment gain has come from increased access, across numerous domains, not just education.) Curriculum and consequence were much nearer a two-year, or higher, college education, as were certification and networking benefits.
NCES does some measures, including very infrequent, but fascinating, National Assessment of Adult Literacy (NAAL), with assessments in 1985 (NAEP), 1992 (NALS), and 2003, covering prose, document, and quantitative literacy. The 2003 survey sampled 19,000 resident adults.
https://nces.ed.gov/naal/
There's a psychology of cognitive development, notably Jean Piaget's (1896--1980) work on stages and level of development, which posits fairly persistent population limits on attainment levels, though I'm only very lightly familiar with the field and current state of knowledge.
Recent studies of computer literacy, however, tend to strongly corroborate Piaget's notions of general atrainment level, notably a 2016 OECD study of computer skills across 215,942 people in 33 countries. If you're in the infotech sector, the findings are sobering. Jacob Nielsen has an excellent write-up, and the study a keystone of my own "Tyranny of the Minimum Viable User" essay.
The upshot is that the needle may only be capable of being pushed so far, and diminishing returns set in early. Increasing access and support at the lowest levels should have vastly greater returns than attempting to raise the highest.
https://en.wikipedia.org/wiki/Jean_Piaget
https://en.wikipedia.org/wiki/Piaget%27s_theory_of_cognitive...
http://dx.doi.org/10.1787/9789264258051-en
https://www.nngroup.com/articles/computer-skill-levels/
https://old.reddit.com/r/dredmorbius/comments/69wk8y/the_tyr...
Direct measures of knowledge and intelligence prove complex.
Q: Does this result in the most educated populace the US has ever seen?
A: Again, by a confluence of measures, I'm not comfortable drawing this conclusion. Fundamentally it confounds inputs (years of schooling), arbitrary indicia (diplomas conferred), and results (population intellectual capacity). It ignores not only shifting academic baselines (curricula, degre requirements, major course of study mix), as discussed, but other factors significant in a political context. A key one being the creation of a small number of tech or other highly-skilled professional hubs, which geographically concentrate educated populations. Given the electoral colleges effective "land vote" (two senate seats per state, regardless of population), education is systemically underrepresented in Presidential, Senate, and (similarly) statehouse politics (both states collectively and internally). This itself considerable dampens effects of education in muany political races and issues.
There's also the fact that educational attainment does not itself seem to preclude leadership in fascist politics, witness those in leadership positions of such movements around the world. A factor which somewhat un-asks the initial question. Mu.
On a number of grounds, I really don't see education by itself as a saviour, thogh it does play some role. More modest than many seem to advocate or hope.
A bit long and wandering somewhat from your specific question, I apologise. Hopefully useful.