Headers in the Mail app.

I have smart names on. If I want to check the address, I normally navigate to headers, find the name, and interact a few levels, then I can get it to show up with a right click context menu, which also has options to copy it. It's a bit of a pain, but I don't see this as a big deal because I rarely need to do it.

Viewing full headers is even more of a challenge, which I had to do a while back when I was troubleshooting a new mail account. Apple really hid this functionality.

I don’t get why Apple hides that away from us. We should be able to check the headers to see who sent it.

At least, not for VO users. Whichever way it's set, you've got to interact with the headers section and then navigate to the embedded object that represents an address. Activate that and you get a little menu which contains both the address and, helpfully, an option to copy it.

If you just want to see all headers for whatever reason, then you've got two choices: you can either choose the option in the Message submenu of the View menu ("Show All Headers", Command-Shift-H), which gives you a filtered and sorted list of all headers in the header area and you need to interact as before to reach the text of the headers and addresses. Or, much more preferable in my view because it shows you the entire, unfiltered, raw text of the RFC5322 message, both message and body lines in the order received, choose "Raw Source" (Command-Option-U) from the same submenu. This is then dead simple to navigate using simple cursor keys and select and copy with standard editing commands and you don't have to do anything at all to extract addressing information. However, this is the raw message, so now you have to perform any interpretation of MIME encoding that may occur in the headers yourself, which is usually not a problem for most cases where you want the raw source like spam reporting or reading the trace fields, but does mean you want to be handy with some command-line tool for base64 if necessary and a knowledge of the relevant RFCs (2045-2047 is a good start, for MIME) would be helpful to understand what's happening.

HTH.

If I'm understanding your question right, you want to know why you can't see the address in the message list, is this right? If so, well, I honestly don't know is the answer; Apple just chose to only display the person's display name if supplied, and the email address only if not. That's not been a problem for me personally, but yes, it does make phishing and scams somewhat easier if you're not streetwise. That having been said, the From address itself, though it is getting harder to forge thanks to current anti-spoofing standards, isn't impossible to spoof either. Depending on the setup of the mail server you use, it might still be perfectly possible to receive a message claiming to come from paypal.com that is not, in fact, from Paypal. Indeed, the same technologies often make it necessary for mailing list managers to stuff the email address of the sender into the display name to avoid forwarded mail getting blocked, making things very confusing. In my opinion the only real defence for this mess is the aggressive use of secret, disposable email addresses where the destination email address tells you where the email came from, but that's another story. Suffice it to say that, for now, you should never trust an email, no matter where it claims to come from, unless you have some other way of identifying the sender, for instance their style, checking the destination of clickable links before you visit them (VO-Shift-U is a great help here) or, ironically, looking at the full headers of the message, as we were just discussing. Suffice it to say, too, that iOS is even less equipped to help you detect these forgeries than macOS Mail is.

I have encountered these problems as well. In gmail it's just one click, show original. I really wonder what Apple think sometimes...

Since you have to open an email, before you can see who it came from. This, of course, can then only be done by tapping on the sender's name, until you are presented with a contact screen with the sender's email on it.
Although, you can alternatively use the action rotor to tap on More, then Reply, and this will also show you the senders email. Without the need to open the email. Still a whole lot of work, just to find out who sent you an email... 🤨

Open the Script Editor, paste the code below, save it in an easily accessible folder, and then associate this Apple Script with a VoiceOver keyboard shortcut.
When you are on top of an email, press the shortcut keys you configured, and a window will appear displaying the full name and email address of the sender.

tell application "Mail"
-- Get the selected message
set selectedMessages to selection
if (count of selectedMessages) > 0 then
set theMessage to item 1 of selectedMessages

-- Get sender information
set senderName to sender of theMessage
set senderAddress to extract address from sender of theMessage

-- Display the full name and email
display dialog "Name: " & senderName & return & "Email: " & senderAddress
else
display dialog "No message selected."
end if
end tell

I wonder if this can be converted into a shortcut for iOS?

But that does look interesting and like it should work.

Kind of a pain, but you can highlight an unopened message in your list, go to File, then Save As. Finally, open the resulting RTF file. Make sure to select Save As. It's the only way to specify the destination folder. If you select Save instead, God only knows where the message ends up.

Can that script be translated for iOS?

macOS and iOS Mail are completely different animals, and the support in Shortcuts for Apple Mail is extremely limited compared to the script interface for Mac, which goes back a very very long time.

Pray Apple don't bring iOS Mail to macOS …