This advice: to write "simply", like much writing advice offered by people who have not studied communication, is pathetic.

Why? Because it offers nothing concrete that can help a given piece of writing or your writing in general.

To illustrate, consider comparing pieces of writing:

A caveat: its hard to set up a worthwhile comparison in the absence of context, meaning external information that pinpoints the points of comparisons. To keep this short, I'll propose and discuss two common comparisons that writers and readers make. Feel free to challenge these instances:

1. Grading tests.

The purpose of grades is exactly to offer a reductionist evaluation that explicitly identifies the "better" answer. Please agree that grading becomes more difficult as one moves from true false, to multiple choice through short answer and finally to essay exams. Taken to the extreme, awarding a Pulitzer prize is a form of grading.

Under conventional definitions of simple, as one moves toward that extreme, isn't it difficult to justify ever calling the simpler answer better?

To me, the limiting case of this claim cribs from Occam's razor. The exact same answer, is better, if its shorter. Again to me, this is a difficult case to make, and ultimately is question begging, because it assumes the grader knows two answers are the same. (Notably to this hacker news community, there is a special case covering whether shorter code performing the same task is better.)

Being more sympathetic to the advice giver (and in line with other comments), the advice really concerns clarity, conciseness, coherence or something similar. It is not controversial to say that, all else equal, the answer possessing this quality is better. (Does this claim require the sameness stipulation? It would makes discussions of that quality more interesting.)

Thus, the advice is either wrong or mislabeled.

2. Revising writing.

Whether stated or not, revision is the signal target of all writing advice. To use the same framework, the author has two pieces, the current piece and a future piece. Of course, the author wants to make the future piece "better"

Leaving the point about clarity and its cousins aside, there are obvious cases where simpler is better. For example, the exact same piece is better absent extraneous material. Put another way, cutting the material only improves the piece if it is extraneous. You can see where this leads: more empty advice.

The bottom line here is that simple is underspecified. It has no value without a much, and probably impossible to formulate, stronger definition of simple.

So, trying to be constructive, what would, concretely, improve a given piece or your writing in general? Try this:

Instead of editing down a given piece - trying to make it simpler - write two pieces for the same context, maximizing the differences between each. This takes time, but it is a much better exercise, especially for the beginner, than going back and forth with the same piece.

I guarantee that having two pieces (not paragraphs, sentences, words or other subsets of the piece) will lead to a much better final piece, even novel, than having one piece and real or potential variants.

Next, and this is the best "piece" of advice, I have: have others read your work - as many as you can, and discuss it with them as much as possible.

TLDR Good writing takes work and conscious practice