In academia, does the amount of material that one has to learn diminish as time progresses?

The first paper I read took two months to process. Now, I can skim through two papers for breakfast. It is not that you get more material to read, but rather you get much more efficient at skipping things you know or recognize as unimportant.

It comes with practice - try reading papers and books, and think about what are the important parts. Learn to identify the 'meat' and which techniques are used. Also, you'll notice that instead of learning 'the stuff', it is about cataloging and storing meta-information about where to find 'the stuff' once you really need it.

After a while, you realize that most of the new papers you read, you only need the gist of it, in order to reference it. Comparably few papers need to be read and understood in paragraph-by-paragraph detail.

_{(Based on my personal experience:)}

On a given, very specific, subject - the rate does diminish; on the overall set of subjects you're concerned with - not so much. Or rather, there are ups and downs.

But the above is in terms of, say, pages, or words. As you learn more, familiarize yourself with patterns in people's work, writing, thought - you catch on faster. If you do achieve mastery of a something, you could get to a position where someone shows you a paper and after a few minutes' thought, if not less, you basically know what it's about, what the implications are and a few likely avenues they have taken to get their results. (But, again in my experience, this happens for some subjects, and in others you may still have the sense of having to part the see every time.)

You used the word "burden" 9 times in your question. My guess is you are learning at way above your comfortable rate.

Once you finish your PhD, in fact once you get through all the mandatory material, you will have much more control over the rate at which you learn new things. You will also position yourself to do what you are more comfortable doing and learning. Learning will feel much less like a burden that is pushed upon you and more like an interesting activity. This way you may keep or even increase the rate of learning, but greatly reduce the effort required to learn new material.