Also compare 1 Peter 2:10 with Hosea 1:6-9.
My own opinion though is that the letter is ultimately written to both Jews and Gentiles.
The list given in verse one is a list of Churches. There is no possible way that any of these Churches had an exclusively Jewish congregation.
1 Peter 1 Peter, an apostle of Jesus Christ, to the
strangers scattered throughout Pontus, Galatia, Cappadocia, Asia, and Bithynia,
Gentiles are found in every nation, so it does not make sense for Peter to described them as scattered. Jews were the only believers where God gave them a land, which is located at Jerusalem, so yes they can be scattered.
The Jews were scattered during the Acts 8:1 account.
But okay, if you want to believe he was writing to both Jews and Gentile believers, I can understand the motivation.
Would you however agree that when Peter said in 1 Peter 4
17 For the time is come that judgment must begin at the house of God: and if it first begin at us, what shall the end be of them that obey not the gospel of God?
18 And if the righteous scarcely be saved, where shall the ungodly and the sinner appear?
Do you think Paul would object to Peter describing the Body of Christ as "righteous" but "scarcely be saved"?
Would he also object to Peter teaching the Body of Christ to expect judgement to begin with them in the future?