I would rather prefer better distinction of the levels of HQs in the hierarchy. I mean that each level of HQ should get its own symbol, not as all of them has just that common "HQ". So, something like this:
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Now that I agree with. While I don't have major issues differentiating HQs, replacing the "HQ" symbol with something more apparent would be nice.
Let's remember that the ingame counters are approximations, not NATO-standard. They are based, if I remember King correctly, on board games they played in the past. I think you'll be rather surprised at the differences if you examine an actual NATO symbol sheet.
I also disagree with the OP - generally my corps are mixed-arms units (as they virtually always were IRL [a Soviet Tank Corps was really a division, composed of brigades]) so differentiating corps by unit type would be useless. What symbol would you like to have for a Corps of 2 armoured, 1 mechanized and 2 motorized divisions?