Why do folding stepladders have "not-a-step" steps?

Stepladders are typically labelled with a warning sticker that says:

⚠️ Danger: Do not stand on top step

or, sometimes on the second-from-the-top step:

⚠️ Do not stand on or above this rung or step. YOU CAN LOSE YOUR BALANCE.

Government agencies give similar advice:

Do no stand, climb, or sit on the stepladder top or pail shelf.

Employers agree that it's dangerous (← don't watch if you're squeamish).

So, why are stepladders designed with a top step at all?

• For waist-height stepladders, I can understand the utility of a top step, as it lets you use the ladder as an improvised sawhorse. Besides, one-meter falls are usually tolerable. For two-meter ladders, though… I don't think so.
• If it's just a place where you can rest your paint can, a fold-out shelf would be better.
• If it's to serve as a hand-hold, then a cylindrical pipe would do — and it would be more obvious that you aren't meant to stand on that.
• If it's for the structural integrity of the ladder, wouldn't a cross-brace serve that purpose without inviting temptation to step there?