I don’t know if this is helpful, but I can’t think of even a single game that I could safely say that every board gamer “must” own. In the end it depends on who is playing and what they enjoy. If you’re trying to cover every conceivable base, then I suspect that the number of “highly recommended” options out there would run to the hundreds; and you might still find that the games you like the best aren’t even the strongest in their field, but just provide the perfect mix of ingredients for you personally.
Basically, I don’t think there’s any correct set of games that you should ensure that you own; so if you’re enjoying playing the games you have, try not to worry that you’re missing out on better ones. There’s far too many to try them all; and even trying all the “classics” would be utterly impractical for most people. If you’re having a good time, you’re already winning.
All that aside, I think Your ideal 3-game collection is relevant.