I had a download handy of REO sales for an area in Ventura, It happened to have the Listing & Selling office ID and Listing & Selling agent ID on it.
Based on that spreadsheet I determined less than 10% of REO sales were within the same brokerage. Of those it was even money whether the listing agent doubled ended the deal. So around 5% (though I noted some from the same “team”).
I bring this up not as a particular interesting take on my area but to say that it would be very easy to prove that agents are ignoring good offers in order to double end deals with the right data. There was one brokerage for example that had 33% deals in house (indicating this could be an issue or they just have a ready supply of buyers) and a REO king who didn’t double end a single deal.