It used to be common for MUAs available on Unix-style systems to support local mailboxes, but that’s no longer the case; and in those that do, it’s not necessarily obvious how to access them.
In Evolution
Create a new mail account (hamburger menu > Edit > Preferences > Mail Accounts > Add). Set your email address as USERNAME@localhost. Disable “Look up mail server details based on entered email address”. Under “Receiving email” set your server type to “Standard Unix mbox spool file” and set the file location to /var/mail/USERNAME. Under “Sending email” set your server type to “None”.
In Geary
Geary does not currently support mboxes. It requires that every mail account has an associated SMTP and IMAP server, so you will have to configure these locally.
In Thunderbird
Thunderbird used to support local mailboxes, but no longer does.
Accessing local mail through IMAP
You specifically mentioned not wanting to set up a local server, but since it's been some years and your requirements may have changed, and I’ll just briefly describe the process. There are three basic steps. First, configure your mail delivery system (such as exim4) to use Maildir format from now on. Second, convert the /var/mail mailbox to Maildir format. Third and finally, install the lightweight Dovecot IMAP server. This will properly read and deliver the Maildir mail locally in a format a modern MUA like Thunderbird can work with. Now you can add a standard IMAP account in your chosen MUA, use localhost as the server, and it should pick everything right up.
Notes
In many cases, MUAs will move email from local mailboxes to their preferred storage, which means you won’t be able to read email using another MUA afterwards. mutt can be told not to do this, I’m not sure about Thunderbird & co.
To test, you can send a local email with mail USERNAME@localhost. Fill in the prompts as follows
$ mail USERNAME@localhost
Cc: <leave blank, hit enter>
Subject: test subject
test body <hit enter>
<hit Ctrl-D>
You can confirm the mail has been received by typing mail. Hit Q to quit the text-based mail client. Now check your inbox via your preferred MUA GUI.