Many of our users explicitly don't want automatically called functions that would slow down the editor (autocommands that map signature requests to the language server, for example), so by nature neovim's core implementation is extremely conservative.
One thing I would like to do, is make the automatic pop-ups for signature easier to implement with our current handler, which means a plugin like signature-x could use our upcoming lsp.config option to configure it's borders (https://github.com/neovim/neovim/pull/14681), and match the rest of the UI.
I also have another project I was working on before the 0.5 stabilization phase (https://github.com/mjlbach/neovim-ui). The goal with this is to have composable/overridable UI elements built into core (which we would use for our internal lsp functions), that can be used (or overridden) by UI plugins.
In summary, I think the likelihood of autocompletion (and generally auto-anything) being built-into core is very small, but providing the APIs in neovim core to make snippets - autocompletion - automated UI elements easier for plugin authors is a high priority.
So IMHO I'd love effectively a dial, perhaps the 'distractions' dial. It's not a binary on/off, it's a spectrum. It could be off--nothing at all distracts me (zen mode basically). It might be on a little bit--perhaps just showing current stuff LSP does by default, errors, etc. And it might get cranked up to max--every keystroke throwing more information at me about what's happening, what am I editing, what's related to it, etc. During an editing session I might move inbetween each level on the distraction dial many times. Kind of like zooming in and out as you're editing a photo.
The only thing that pops up by default right now is diagnostics.
Perhaps there are ways to tweak lsp_signature UI... but at this point, I chucked it all and went back to coc.nvim which does it all (suggestions, signatures, etc.) all with the same UI.
Make it like that--make it work with all UI out of the box and not make me dig through tons of plugins. That's my honest suggestion. Sorry I'm not joining a discord, etc. to give this feedback.