Personally I still use SeaMonkey - same underpinnings but 1. the underlying browser is available as a browser and 2. my reaction to the T'bird interface isn't that it's old, it's that it's too ugly modern*. But would I be prepared to change to an updated T'bird?
Yes, provided it really did involve a ground-up change.
Let's start be recognising that for the user the principle object of communication is the thread**, not the individual messages that comprise it; a singleton message is just a member of a thread which has, currently, no additional members.
In the SM/TB interface the thread is a run-time construct of any linked messages in the mbox file whose contents are currently being listed. By default a sent email goes into a separate, sent mbox. Unless the user discovers how to change this default the thread as shown doesn't even include their own contributions.
So the first step would be to add any incoming or sent message to an existing thread to which it belongs or create a new thread if none exists. The next would be to preview the thread contents better; show the first two or three non-quoted lines with the option to extent and reply. Something like el Reg's comment presentation, in fact.
Next, let's remember the numerous comments on here from support folk who discover users with thousands of read messages in their inbox or deleted folders. A good UI would confine inbox use to unread message Opening a message would remove it from the inbox. There should be another folder for current mail threads. After a period of inactivity; no further messages on the thread during the period would result in its being archived although there might be some sort of staging folder for recent but non-current threads. And the deleted folder is nothing more than a guard against those oops! moments, it will be cleared according to some sort of schedule.
That would be a start but there's scope - and, I think, need - for a much more radical approach. It's a typical email client and AFAICS no email client has got beyond being a thin wrapper around a basic utility to exchange messages with a server.
* i.e. UI components without clear boundaries and scratchy monochrome icons that look like a cuneiform writer's first attempt at heiroglyphs
** Thread, conversation, discussion or whatever you prefer.