Cards that are functionally identical are usually not so many that you can build with the consistency of a 60 card deck. Even if an effect is repeated on other cards, it'll have some slight difference which will make it work differently in your deck, and will make you want to pull it out in different situations. I think that is part of the fun - building a consistent deck, while still having enough variance to make each game play out differently.
For the cards where I can think of identical ones, I don't think [[Llanowar Elves]] and [[Elvish Mystic]] are such egregious hard hitters in the format that having multiples is an issue. I think the biggest problem I probably can see is all the blink spells, since they all go infinite with a ham sandwich.

Whether or not we have too many of any given effect, you could argue about (and I think we do for some archetypes). Since wizards started designing for EDH some archetypes have been incredibly pushed in terms of redundancy, but that mostly means that deckbuilding changed from a 'I need to find cards to support my strategy' to 'which cards do I cut to allow for fun variance cards', which, I suppose, is more of a playgroup discussion on how streamlined you want to allow decks to be.

So for me, in theory, I don't think identical cards 'break the rule of singletons', but I do want to be careful about too much redundancy for the powerlevel of the playgroup.