As a potential counterxample for when you might want to remove numbers, a couple weeks ago I was presenting a proposed analysis pipeline for some data, and what I'd expect the results to look like. The x-axis points were all fixed, and clearly tied in to numbers I had discussed previously, and the y axis had experimentally meaningful ticks at 0, 1/2, 1, and 2.

I was, in fact, told later that the xkcd style graph was extremely helpful in conveying that it was not a graph of real data yet.