I suppose that when someone talks about an exim expert on this list they might be referring to me.
Though I don't consider myself an expert, only someone who has attempted to understand Internet email since it existed, and who now uses and likes exim.
That said...
hostpc.com, you're showing us excerpts from maillog, which says nothing about how exim processes email. Forget about it. Look in the /var/log/exim/ directory for mainlog and for rejectlog. Note that the lines in rejectlog are also in mainlog, but it's a lot easier to grep them, read them, understand them, when they're in a logfile of their own. Note also that you can change the various exim logfiles to show whatever you want; the current exim logfile configuration is the one I decided on over a year ago. If it doesn't work for you, feel free to change it.
And if you want us to be able to consider your logs when attempting to help you, send us no more than 100 lines from rejectlog.
Now let's look at the post. Is 55,000 emails a lot? Perhaps. None of our accounts does that many in a day. Should it affect your server? Perhaps. You didn't tell us how powerful your server is.
It's up to you to decide whether or not you want to keep customers with that kind of load.
You may want to disallow any other catchall setting besides "fail"; though we don't have a problem, perhaps you do.
The problem with a catchall account is that all email from dictionary attacts will end up in the catchall. Practically none of our clients still use a catchall account, though many used to before spam became such a problem.
Are you using SpamBlocker for any of your domains? You'll find that SpamBlocker will block over 80% of the spam, even from dictionary attacks.
How do you know this account got all those emails? How did you count them?
Presuming they did, you may certainly decide you don't want accounts with that many emails; that's certainly a decision you can make.
And you may certainly shut off an account going over your limits, as long as you make your terms clear to your clients before you exercise them.
I've said it before, and I'm saying it again...
Use SpamBlocker. Then use SpamAssassin.
If you've made changes to your exim.conf file you may want to download a new one, or wait another day or so until I issue a new one (it was to have happened tonight; it might still, though I doubt it).
Jeff