I think the pub story is simply an everyday example. It serves merely to illustrate the idea. There are clearly much better ways to get the message across and in that sense the story is wanting.

AFAIK the most 'and's you can have in series is five. This is because it is only appropriate to use the word and when dealing with two items. Here we have two sets of items, each consisting of a pair of items one item in each of the sub pairs is also 'and'.

You can't continue to add subsets without creating a list, in which you should list the items instead of saying or writing 'and'. Hence the maximum of five given in the example story.

In structural terms: (Bell and And) and (And and Whistle)

I think the pub name is also a subtle play on the idiom.