The problem is that a lot of the time it feels like meaningless platitudes. Like they feel they have to say something out of politeness but don't actually want (or able) to help you.

What would have been better? To just say "I'm sorry you're having a hard time". If you don't mean something, don't say it.

^^^^^^^^^^^^^^^ THIS

While it may seem like I am being oversensive about the subject, it is understandable because I left out a large part of the context. When you have heard of this phrase hundreds of times over multiple years by people who were not in the position to help you in the least bit, it becomes a meaningless platitude.

Are you assuming/implying that the people who say "let me know if you need anything" don't actually mean it? Because I don't believe that's generally the case, especially if they're actually friends and not just random acquaintances.

I don't personally say that sentence outside of a work context; usually I would say "call me if you need to talk", but I won't take proactive action unless I believe my friend either wants me to or need me to.

At the end of the day, someone makes a choice to interpret this as a platitude. How about taking up the person on their offer?

Let me try to explain - I've had cancer at a relatively young age, so heard that a lot. I wasn't visibly sick, i just knew there's a chance I'm gonna die in the foreseeable future from it.

Unless the person saying it had access to some experimental treatment my doctors don't know about, there really was nothing they could have done to help me. I knew it and they knew it.

So while I didn't get angry at them (because I knew they said it because didn't know how to react differently), it did annoy me as it was basically an empty promise.

Right, i was specifically outlining depression. Taking care of a sick person, i would also err on the side of giving more specifics eg. "Tell me if you want me to get you groceries or something".

But there is a difference between empty platitudes such as "thoughts and prayers" and a genuine albeit abbreviated "I'm your friend and I love you, I don't know how I could help you, but if you know, don't hesitate to ask on account of it being too much."

It seems like it's hard to understand how "let me know if you need anything" is hard to hear unless you've heard it hundreds or thousands of times.

I'm sorry about the situation you are/were in. That must have been very difficult.

It's not for you they say it, but for them and or others. Or to put it more directly, you don't say it for them, you say it for you.

It's like forgiveness, if you forgive someone, the main benefit is to you. By forgiving someone you take a load off your own shoulders. It's often meaningless to them if those forgiven know they are.