You're conflating two different things here.
All degrees are the same - of course not. Some are more academically rigorous than others, different modules, etc.
If this is relevant it's taken into account, but we're talking about generalist schemes here.
Where you're going wrong is equating academic achievement to motivation, capability, and other personal traits. You have a very simplistic view, stating that 'everyone' has the same chance in exams. Are you really saying that a well-fed child, with a warm , quiet comfortable home to study in. Has the same chances as a young carer has to look after a parent and possibly other siblings? You acknowledge differences in parenting and schooling but are somehow blind to how this affects exam performance.
Not only that, the ability to focus and pass written exams aren't what's valued in the workplace, beyond a minimum standard. I've interviewed many bright graduates, even from Oxbridge who were clearly very intelligent. But they couldn't communicate effectively as a team, lacked common sense and resourcefulness. Could only 'work hard and focus' when they had set goals. They didn't do so well in a workplace setting with competing priorities and vague targets, interpersonal conflict and changing deadlines.
As employers, we have our own tests to ensure that employees are capable. We interview students, talk about their past experiences, etc etc all of that build a complete picture of a graduate.
The Big4 accounting firms for example are mostly CV blind now and the majority of their graduates, even from erm 'lower ranked' universities pass difficult professional exams while working. They're clearly capable.
Also if you look at a lot of 'top surgeons' they didn't go to the 'top' medical schools but they're all qualified and obviously skilled and capable. If you prefer a university name instead of professional achievements, go right ahead.
FYI I went to LSE , my best mate's currently doing a PhD at Oxford (after a Masters in the same place) and we can 100% confirm.... The book smarts are not always the best hires.