I have heard this sentiment a lot and tried a lot of email clients and personally I still don't enjoy using any email client for this task. A properly designed forum software is always going to be easier to use for its express purpose than a mail client.
Which email client does?
It has some restrictions that I occasionally want to relax though. It doesn’t keep a complete database of all message ids it has seen in your inbox, just a list of the ones it most recently pulled into a summary. For example, if you pull up a summary that includes the latest 100 messages in your INBOX, then the links will take you to any message within those 100, but clicking on a link to a message older than that just tells you that it can’t find the message id in the summary.
You seem confused. Signing up to multiple mailing lists won’t require you to have multiple email addresses, and at the same time they don’t require you to subscribe using your main email address either. Many email hosts will give you as many mailboxes as you like, either using plus–addresses or just new mailbox names.
> And then how do you link to users or messages from your email client?
Every email has a unique message id. Simply include a message id in the body of the email, and your email client should turn it into a link (provided you happen to have that message available). If your email client doesn’t do that, perhaps you need a better email client.
> They are unbrowsable and who likes getting their inbox spammed in order to follow a discussion?
It really sounds like you need a better email client, or you just need to learn how to use the one you have better.