Why in the Run dialog in Windows 7 there is still one button?

Because this can be done by pressing Win → (enter exe-schnick) → ctrl+shift+enter.
Simple user from admin should be run rarely, and the rest about this hotkey as you like.

I for such purposes use the shortcuts:
\rCreate a Command Prompt Shortcut with Admin Rights

If I'm not mistaken, but the "OK" button with the shield and is run with administrator rights

MS Corp. you need to read the section on habré user interfaces :)
Well, so try to unsubscribe they say, even on the phone, but sometimes the answers are stupid, a friend called and told him what you have in Russia a lot of piracy and therefore.

Could be because Microsoft hadn't thought of? Maybe you should write to them to technical support and not here?

I think the problem is far-fetched. Most programs that require elevated rights, ask about them yourself. And if you really needed to run something on behalf of the admin, better to let the user find the desired program and poke, right-click — an extra level of protection from the fool. In my experience, similar start required 2-3 times for a couple of years in exceptional situations. Why push this in standard interface but still on first place?

If you disable UAC, all run using Win+R runs as administrator. If you do not want to disable UAC — the only way — as described above, using the Win key and typing in the search bar