Mailing lists I access with my preferred mail client and environment.
Receiving "10,000 emails per day" would only happen on a very active list. In most cases you're talking about a dozen or at worst a few hundred. Your email client can easily filter those into a virtual folder, and quickly find the messages where you are addressed or threads you're interested in.
Once I have the emails, I have them forever. I am not dependent on some forum remaining online five years from now if I want to go find an old message.
Web forums and wikis just suck for message-based interactions. Email is designed for that and it works really well.