Exactly, we all want to be recognized as road users with as much right to be on the roads as anyone else. So, why shouldn't the same rules apply when it comes to using the roads when under the influence?
Pedestrians have an absolute right to be on the road.
Cyclists, by virtue of the greater danger they pose other road users, have some restrictions on their right to use the road (e.g. not allowed on footways, must have lights at night, shouldn't be incapacitated through drink, etc)
Motorists, by virtue of the yet greater danger they pose other road users, have even more restrictions (e.g. must pass test and get licence, stiff limit on alcohol, MOT, insurance etc)
You may be under the impression that motorists are the rightful owners of the road and everyone else should fit round them. Although practically speaking this may be the case today, historically it was not the case, legally[*] it is not the case, and it's clearly not desirable (in view of CO2 levels, urban congestion, lives lost to RTCs etc) that it remain the case. I would therefore be very opposed to any measures that seek to reinforce the status quo at the expense of people who do not have the good fortune of an outsize tin box to cart themselves around in.
[*] hypothetically-legally in the sense of "good luck finding a CPS that'll bring the case and a jury who'll convict"