AppleScript for counting messages in Inbox fails with "Can't get mailbox"
Your mistake is understandable in what you expect should be the syntax.

Each account has it's own mailbox named "INBOX"

In Mail the mailbox  inbox  is the reference to the top level inbox that shows contents of all other inboxes named "INBOX"

2 examples:

Example 1

tell application "Mail"
    set inboxes to first mailbox of every account whose name is "INBOX"
    set messageCount to 0
    repeat with i from 1 to number of items in inboxes

        set this_item to item i of inboxes
        if this_item is not missing value then
            set thisCount to (count of (messages of this_item))
            set messageCount to thisCount + messageCount
            log thisCount
        end if
    end repeat

end tell
log messageCount


Example 2

tell application "Mail"
    set messageCount to (count of (messages of inbox))
end tell

log messageCount


Both return and log the same total. 

But example 1 also logs the individual count of each "INBOX"

A good place to start is to read through:  AppleScript Fundamentals