Following are a few reasons why I believe that the angels refer to ministers of the churches rather than to heavenly angels:
As has already been mentioned, the same Greek word translated "angel" at times refers to men: John the Baptist (Matthew 11:10; Mark 1:2), John’s disciples (Luke 7:24), Jesus’ disciples (Luke 9:52), and the Israelite spies (James 2:25). Granted, someone brought up the excellent point that in these instances the translators always used the English word "messengers" and not "angels." That point was not missed by me.
John was instructed to write to these messengers. There are no other instances in the Bible where we find men writing to angelic beings.
Jesus gave this Revelation to John by His angel. "I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, and the bright and morning star" (Revelation 22:16). If these messengers were heavenly angels it would mean that a heavenly angel wrote a message to other heavenly angels. Again, there is no biblical precedent for this.
Nowhere in the New Testament does it teach that a local church has a special angel messenger. It does, however teach that the church's messengers are men, either the pastor or elders or other key men. For example, the messenger of the church at Philippi was Epaphroditus. "Yet I supposed it necessary to send to you Epaphroditus, my brother, and companion in labour, and fellowsoldier, but your messenger, and he that ministered to my wants" (Philippians 2:25).
These messages from the Lord to the "angel of the church" address them as members of the churches when Jesus says, for example, to the angels of the church at Ephesus and also at Smyrna, "I know thy works" (Rev. 2:1-2, 8-9).
There is no instance in the New Testament of angels addressing churches.
If these are angelic beings, it would mean that they failed to keep God’s word perfectly, which is impossible. "Bless the LORD, ye his angels, that excel in strength, that do his commandments, hearkening unto the voice of his word" (Psalm 103:20).
I realize that my whole post can be dismissed with the "literary device" card. I expect it to be so.
Good day, Gentlemen. 8)