I think it is clear that people with high reputation scores get more upvotes because people assume (usually accurately) that they are correct.
It's not clear at all.
Please post a list of questions where incorrect high rep user answers are voted above correct low rep user answers.
If you can prove that this is happening (and if it is "clear" then you should be able to find many examples of this) then I'm sure people will discuss what should be done to combat it, including your suggestion.
If you can't prove it, however, then your suggestion, like all the other similar suggestions for the same perceived problem, will remain unimplemented.
Given that this type of behavior should be detectable without making the change first, there is no reason to experiment.
If, however, you are only putting forth your theory that correct high rep users are voted above correct low rep users, well that's been hashed to death in other questions, and this one should be closed as a duplicate of existing questions.
Lastly, you don't have to play the 'rep' game, but if you choose to do so, high rep users are in no way holding you back. There are a lot of users that have quickly climbed the ranks over the last year and now lie in the area you might consider "high rep" - so even if we assume there's a voting disparity it doesn't prevent someone from progressing at whatever rate they are capable of and choose to attain. Keep in mind that the rep cap really does level the playing field.
Here, let's do this:
Straight line. He has the same ability to get rep as a under 1k beginner as he does as a 40k high rep user a year later.
How about https://stackoverflow.com/users/12960?tab=reputationhistory#tab-top
Same result. There is no difference between them in terms of getting more or less rep at a higher and lower number, and both of them reached 40k in under 12 months. That's an average of 120 rep per day, so it's under the rep cap, generally. The line isn't straight because of the rep cap, it's straight because it's just as easy for them to get rep at a lower level as it is at a higher level.
Let's go for some that accrue more slowly, like https://stackoverflow.com/users/65696?tab=reputationhistory#tab-top
Interestingly, this graph shows that it was easier to get rep at lower levels than high levels. Further, he still will reach 10k rep in about a year.
Same story. Easier when first starting. It may well be that these two examples are simply people who are spending less time on it as they go on, more research would be required to normalize the data.
What's similar in all the above examples? There is NOTHING preventing ANYONE with experience and skill from progressing up the reputation ladder.
At best there are a lot of people who want it to be easier to climb the ladder without doing the work, and/or without having the skills, and/or without having the clear communication skills that this site rewards.
I disagree with removing the reputation scores as they are an earned badge of honor, and one of the reasons why some people work so hard to give good answers to thousands of daily questions.
But what I really don't understand is why people are even complaining about it in the first place. Three thousand people have demonstrated that it's easy enough to get 3k rep in under a year, five hundred people have shown it's easy enough to get 10k rep in a year or two, over one hundred have 20k in 1-2 years, and so forth.
Let's assume it's really happening. SO WHAT? It's unfair? Ok. SO WHAT? That high reputation has been earned! Some people complain about there being a cycle of the rich getting richer, but if you look at a graph of reputation there's absolutely NO break, gap, or even a valley between those with high rep and those with low rep. There's no cycle, there's no "rich getting richer."
The only complaint I can see are people saying that the function of earning rep given the same answer input is also a function of existing rep, and that it's not linear.
waaaaaaaaaaaaaaaaaaaa - my functions aren't linear, and there's a feedback loop! This game sucks!
But it's NOT EVEN HAPPENING. So far everyone that has complained has ultimately admitted that they simply "feel" that it's harder. They "perceive" a problem. No one has offered to do the work of performing a double blind study on the site - rather they want their idea implemented, believing it will become self evident.
If it's really that important to you, then do the work and prove it. Don't expect the site to change significantly just to disprove "your perception of bias."
And even then, well thanks for finding the mathematical model, but that doesn't mean we need to change anything. Past 10k there are no additional benefits. Does it really matter that the function is more complex than what you want it to be?