Could the same thing not be said about people who WALK after consuming alcohol? You are suggesting the use of a sledgehammer to crack a nut IMO..
There
are laws pertaining to people who walk after consuming acohol - well, sufficient alcohol to be drunk. Just being drunk in a public place is an offence. You don't have to be disorderly.
And no, you can't drive a steam engine while drunk, to all of you thinking of exploiting a loophole. Or be in charge of horses or cattle. It's da law.
I'd have thought that a drunk on a bike would be significantly more danger to themselves and others than a drunk on foot. But the drunk at the wheel is
so much more of a danger than either that it really does warrant special specific laws.
Incidentally, I was driving in Finland one morning and there was a police checkpoint where
every car driver was being breathalysed. Only took a few seconds. A good idea I thought. But if they tried it here there would no doubt be prolongled bleating from the Top Gear tendency (and on here too, if it included cyclists

)