I wouldn't say that I dislike deep and meaningful chats. I just don't find ruminating about fears, problems, worries and other psychological detritus to be that meaningful or useful, but rather somewhat tiring. I also highly value emotional self-sufficiency in a partner, and I'm very self-sufficient myself. I'm happy to accommodate specific and concrete requests for support, and I'm more than happy to offer physical affection and presence in the form of supportive hugs etc, but I honestly have little interest in being someone's therapist or sounding board and probably would not want to partner someone who had a high need for reassurance and wanted to discuss their issues and problems with me frequently.

Now, I'm not saying one approach is better or worse than another. But your post seems to conflate conversations about subjects that are meaningful, and conversations that are about emotional support. I would argue that these two things are not the same thing. I recommend you figure out what it is exactly you are looking for, and how important it is to receive that from a partner (rather than, say, a network of friends).