Ok, so there's a flaw in your way of thinking. I'm not saying you are wrong in the part of 'people wanting to help sad people to get happy' but I think you do not understand what is the best approach in helping someone who is actually in a bad place mentally. But first of all, no judgement or anything, this is what a lot of people do, it comes from the heart, has zero bad intentions.

So, when someone is feeling bad, no matter what form, there is a reason why they feel that way (unless there is a chronic disorder or mental illness, but even then there can be an underlying cause). For example, someone they love passed away. People unconnected to the person who passed (so are unconnected to the event and the grief process) see someone feeling sad, so they don't know how to deal with it and try to make them happy. They see someone mentally in a bad place, and want them to not be there but instead to feel joy and happiness. This is understandable. However, for the person who just lost a loved one it feels completely different. They just lost someone they love, which hurts. There is a whole process, the five stages of grief, which is something you cannot force onto someone but which costs time to get through. Someone trying to cheer you up while being in this (healthy) process feels like a clown at a funeral. It feels totally wrong. You need to feel this way, you need time for this wound to heal. Feeling bad is a wound which needs proper care and time to heal. When you force it, you make it worse. Even when the intention is good.

I gave an example of someone passing away, because that is something we all have to deal with, and many already had to deal with. But any other reason for feeling bad, whether it's a loss of a loved one, a relationship breakup, trauma, failed exams, abusive parent or anything, they do not need someone to make them happy. They need someone who is there for them, who listens, who does not judge, who is ready to try to make them happy as soon as they are ready for it. Their feelings of sadness need to be there, they need to process, they need to get a place in their life.

There sure are moments when someone needs a friend to pull hem out of their sadness but there needs to be room for sad feelings too, because unsolved sad feelings will marinate and come back even stronger.

When a friend of mine feels bad, I give them options: "Would you like to meet up? I'd be there for you. We can either 1. Talk about it, 2. You talk to me, I just nod and say yes and agree with everything, 3. We do not talk about it, we just watch a movie, have some dinner, do something stupid, whatever just to not being alone for a bit without having the pressure to explain."

When I see a friend feeling bad for a long time, I try to talk about it to try to pull them out of a negative cycle. But I never try to make them happy. Because the only person who can make them happy is themself, I can only be a part of that process.

My friends do the same for me, which is the reason why they are the only ones I consider my true friends. Because we can be there for each other in times of need, without pushing forced happiness onto each other because society wants to force everyone to be happy. I can only be happy when I'm allowed to feel bad and to process those feelings.

So I understand anyone who tries to make a sad person happy, but often it's just not the best approach. Impact always weighs heavier then intentions. I do use it hold it against people when they do this, it's just something I cannot deal with when I feel sad because it doesn't help me in any way.