Within a job ladder, you then have levels. They tend to map onto
years of experience, *whether you have a degree or not*,
what kind of degree it is, how well you do in your interviews,
how much money you ask for or hint about, and possibly how
well you did as an intern.
As my manager put it at the time "Nobody gets promoted for reducing the size of a tire fire by 50%".
You have to be really strategic about what you work on, and for who. It's not about the technical contributions, it's about finding and retaining a sponsor higher in the organization. You help them torpedo competing initiatives and increase the headcount they manage (headcount is points), and they help you navigate the political climate to get onto the project du jour.
I worked at an old school BigCo for 3 years and we shipped not a single product from a team of ~300 people if you count peripherally involved people. The only thing that saved us was that we managed and maintained a small software tool used directly by the CTO of the conglomerate, which we could wave as a ward against interference.
Some of those 300 got promotions, some got transferred (far away from their home and family, into different divisions that they had no experience with, aka exile), and some got laid off, even though as far as I could tell none of us had any ability to affect the end result (priorities changed too quickly to make any headway). For the record, I quit.
Mean time between reorganizations, management shakeups, and goal shifts was ~2.5 months.
I've been stuck as "the guy who quietly fixes the problems no one else can figure out" for years, while being passed over for promotion because I'm not sufficiently externally visible in that role.
... and then they wonder why there's so much turnover in our industry. "Due to circumstances completely outside your control, you have no future at this company." "Hm - well, maybe I have a future at this other company then." "What ever happened to loyalty?!"
Of course there can always be problems with skills or performance due to not having a relevant degree.
But I think with many years of experience this requirement can be replaced. But that's not "right after you get hired"
She left high school early to go straight into college, so officially she never graduated from high school. That's an automatic rejection from many companies, even for "white collar" positions. It doesn't matter that she's studied at some prestigious places, has a post-graduate degree, etc., because there's an unchangeable, un-bypass-able filter at the start of the process which rejects anyone who doesn't have a high-school diploma.
I'm not one for dishonesty in general, but if you have a post-graduate degree from an accredited college, ticking the box on an application form that you also have graduated high-school is damn near not a lie, IMO.
Like @paxys (sibling comment), I've not seen it be a problem once you're in, but it does affect the ease with which you get job offers, and those can be a big part of career growth.
Sometimes you land a great job, in a great company, with a great manager and you work your way up, with the right opportunities at the right times with the right rewards.
But most people find that they run into a blocker somewhere along the way. Maybe the company isn't growing fast enough to create relevant oppportunities. Maybe you get a manager who sees you as irreplaceable and doesn't want you to move up. Maybe something stuffs up and the blame falls on you and your promotions get stalled for a while.
And in all those cases (and more) it helps to have a ticket out of there. Even with 5 to 10 years of experience, some % of hiring managers / recruiters will look at where you got your degree (and in what discipline) and take that into account when deciding whether to interview you. And fewer interviews leads to fewer offers, leads to fewer choices, leads to less control over your career path.
The lack of a degree is not a total blocker - once you get into that first role and prove yourself you've got good chances - but it will have some impact and could make it harder to meet your goals.
If you get in without a CS degree, you often can get looked down upon as "not technical" or "more business than technical" unless you prove your chops coding.
Of course, one has to ask - how many people today have a CS education before they even reach college? It's possible that somebody already has CS education from high school and chooses to study something else to broaden their horizons.
Unfortunately, that can be a costly mistake when applying to jobs requiring a CS degree. But it can pay huge dividends in one's diversity and understanding of the world.
Places that really pay attention somewhat ignore your degree or education and focus on your skills and/or experience, IMHO.