I really don't have a clue as to what my parents would have decided to pay for versus requiring me to take out loans for when I was applying in 1976, had I not wound up going to a super-cheap (albeit not a commuter school for me) college that probably cost (all-in) the equivalent of $20-25k/yr in 2023 dollars that they paid for. In any event I was the beneficiary of my parents' generosity and while I did have some college jobs and take out some minor loans, I definitely did not 'pay my way' nor did I expect our daughter to do so. My ex, on the other hand, got very little financial (they let her live in their home while she got her AA) and less emotional support from her family - she was the very first in her family to go to college at all (and to her great credit, went on to get various professional degrees as well as a Ph.D.!) and definitely 'paid her own way.'
My ex and I took the following approach with our daughter: We would be willing to pay up all costs, including on-campus residence, at any state college where the tuition was under $20k - this was when Michigan and perhaps other states had started soaking out-of-staters with ~$45k/yr tuition for undergrad, but many other states had more reasonable surcharges. We'd also pay if she went to an elite institution that was arguably 'worth it' in future prospects, either academic or for earnings potential.
As things transpired she was not particularly academically inclined in high school...after graduating HS she started at a commuter college, then transferred to a state college where she lived on-campus, became more focused in her studies, and graduated... without loans. Our costs started lower the first year thanks to commuting, and then went up to about $20k/yr (around $30k/yr now, based on what I see on the SUNY webpage).
As far as the 'I paid MY way through college' thing goes...
We all have been benefitting from lower tax rates in our working lives versus what were extant in our childhood - for example when i went to college in 1976, the marginal tax rate was 28% for a MFJ income of $18,500 (equivalent to $100,000 today). Now, the marginal tax rate is 22% for MFJ income of $100,000. That reduction in federal revenue has almost certainly led to reduced revenue sharing with states, which in turn pressures them not only to increase state college tuition, but to build enough new schools and classrooms.
When you couple the price pressure on one side and couple it with increased demand (both more kids and a higher percentage of them wanting to go to college), you get a surge in prices beyond what inflation alone would have driven; this is exactly what has indeed happened - costs are way higher now. So anyone thinking about their ability to pay their own costs way back when, versus what is involved now, is not comparing apples to apples.
However, if you took that $6k in tax reductions [(28-22)x100k], saved it over your working lifetime, and saved it each year, and then took the proceeds and applied it to your kids' college costs, I'm pretty confident that they could 'pay their way' through the rest of the costs. So declining to do at least that for your kids is on some level... making your children pay for your lifestyle.