So removal of pain does remain a goal even if we can be "happy" without it, since we want to be even happier and have more pleasures to achieve complete happiness where nothing torments us and we can enjoy pleasures undiluted.
I agree firmly with the idea that getting completely rid of bodily and mental pain constitutes the goal, and that having such a goal serves a very real purpose as identifying an organizing principal, and as I think that you mentioned earlier this is part of the "gods" analysis - the gods serve as a way of thinking about shooting for the highest possible goal.
All of these concepts have details about them that help us use them as targets that we'd like to approximate as closely as possible.
Probably the real practical problem is that as humans we can't practically speaking avoid all pain (and I know you are very young wbernys so speaking as someone whose a lot closer to his end than to his beginning the pains really begin to stack up the older you get!).
I think the struggle occurs because many people would like to have a firm set of Do's and Don'ts -- Ten commandments so to speak - that would prioritize for us exactly when some pleasure is going to cost more than its worth. The natural/necessary categories help with that, but even there we don't have a rigid set of rules like the religions tend to offer.
And in the absence of set rules, people struggle with whether they should "avoid pain at all cost." I think the friendship example, or lesser questions such as "Should I get a dog even though he'll only live maximum ten years and then I'll be heartbroken when he dies." helps crystalize that yes, we DO choose things that we know will cause us pain when the pleasure we get outweighs the cost in pain.
Just brainstorming here but it would be very helpful to come up with other illustrations of the same principle (examples of discretionary actions where we clearly choose to accept some pain). We often use the examples of "going to the dentist" or "getting surgery" and those are useful, but to really dramatize the point it would be good to point to examples where we could walk away from the situation without pain, but we choose to go forward anyway (friendship, pets, etc......)