It's a different type of blotchy. If you do a search of mdf and how to finish unfinished edges, you'll see its a bit of a problem with mdf. Since mdf is quite absorbent, if you put anything on the unfinished edges, the grain swells and "stands up". Even if you sand it back down, when you re-apply, the grains stand back up, giving it a rough uneven texture. It looks a little like uneven colored velcro.
You can apply like 10 coats of sandable sealer and eventually get over it--personally I think edge trim tape is the easiest.
Trust me, I've done a fair bit of experimentation. Leaving it unfinished really causes the edges to stick out like a sore thumb. Trying to finish it over with wood filler, wood glue mixtures, tons of primer, oil-based sealers--all jacked up the price and the time to finish.
On the flat finished edges, MDF is a wood product, so it has a certain grain and irregularity. If it looks nice, you call it "character"--if it doesn't you call it "blotchy". I can in fact paint over the whole thing and even achieve a glossy finish if a customer wanted. But that would require about 3 cans of primer and 3 cans of paint, and a hell of a lot of sanding.
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