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The only penalty that will ever work is immediate physical punishment. Put those small "speed-bump"-like curbs like we see in chicanes to avoid shortcutting.

Cheap, easy to install, doesn't impede advertisement, and drivers who really lose it just have to either slow down or take an even longer route before rejoining. Problem solved.

This is if they absolutely have to keep that stupid run-off. I have never seen any driver actually losing it to the outside of a hairpin exit. It just never happens and can't physically happen, you either overshoot it at braking or spin to the inside on throttle.
They could just put a wall there and nobody will ever hit it, see Canada hairpin or La Source before they (horribly) modified it.

No. If there's tarmac everywhere, the car will just destroy itself on the bumps, perhaps fly a bit but it will never get enough height to clear the fence or start a flip, that only happens in gravel traps and bumpy grass.

I was actually talking about slow corners but there be it, put them there too, explode those front wings like gravel used to do. This is F1, not a racing school.

Alsonso did that a few times, but I remember Vettel doing that all the time during the last grand prix, especially when he was closing up to Button. How many replays were shown with Vettel taking a very wide line? And a few times I saw this happening in the background, but no replays were shown. I think Vettel did most of this 'off the track racing'. Alsonso did that too, I won't deny that.

Button I think I can't remember doing that.

like many have said, the only sollution would be to have a few metres of another material (grass? grind? something else) before the actual tarmac run off area. so that going wide would automatically be punished somehow...

Based on feeling more than actual laptimes it seems they didn't gain anything.

It looks difficult to get any benefit considering the corner angle, unless you go all DTM on the runoff but I doubt it's possible with an F1, at least nobody attempted it!