Surely something should only be an offence if you're not supposed to do it, and if it is an offence then aren't the police obligated to enforce the law? Otherwise you're left with the bizarre situation where there's lots of laws, all of which we're supposed to abide by, but which are only selectively enforced at the whim of the officer concerned.
Unfortunately there will ALWAYS be more laws and more offences than the police can possible deal with (if they went on a "work to rule" they'd never get twenty yards out of the police station before dealing with some trivial shite).
The fact that every officer has absolute discretion in enforcing the law is a key part of the police - public relationship in the UK. That is, I think, a very powerful aspect which helps maintain the relationship (there are thousands of people (including some on here)) who tell stories of how they
could have been arrested but were let off with a bollocking / given a lift home or whatever. This is the entirely reasonable basis for the "attitude test" - if someone is committing a minor offence and the officer is willing to deal with it by way of informal warning, they are perfectly entitled to take a step back and say "OK, if thats how you want to play it, you're nicked!" if their initial approach is met with snarling, spitting abuse and violence.
You mentioned two very different scenarios - one in which the exercise of discretion IS appropriate and one in which it would not usually be. In the first there is no VICTIM as such (e.g. drunkenness), in the second (e.g. theft from a vehicle) there IS. In the latter case, if the officer did not intervene and pursue a proper investigation, etc. the victim would be able to complain about them failing to do their duty. They could
try to do that in the first scenario (and some interfering twats do try!) but they'd never get it off the ground in the Courts unless they could show some specific harm being caused.
There is a grey area, which you touch on in the last part of your post and that is where individual, non-victim offences (such as drunkenness) have a wider impact (e.g. widespread drink fuelled disorder because pubs allow drunkenness (it is a very specific criminal offence by licensees, etc. to allow a drunken person to enter or remain in licensed premises, or serve them alcohol, by the way). In these situations police may well have a bit of a local crackdown although they will normally try and make sure that individual's caught up as "collateral damage" (e.g. individual users caught buying as part of an operation aimed at a drug dealer) are dealt with as leniently as possible.