Is there any way I can hide the chat messages that almost all addons produce?
That would be very difficult due to the way addons produce chat messages. For example, some addons send messages via standard channels like the raid channel for those annoying loot addons. You would need a custom filter for that specific addon.
For addons that just write directly to your chat box, that might be more doable, but it would probably require you to make a new chat window, hide the default chat window, and have all the messages you care about sent to the new chat window.
One simple test you could do is to make a new chat tab, select all the channels you care about in the filter settings, then use that tab instead of the main chat tab. The messages would still show up in the main chat pane, but you wouldn’t see them because you’re on a different tab.
Possible Solution:
Right-click your General chat tab. Select to Create New Window. Name it whatever you want, like “Chat”, then click Accept. That should create a new tab on your main chat window. Select that tab. Now all of the addon spam will stay in the main tab while you can just see the chat channels you care about on your new tab.