Edu & Arteta tried to sign Tammy but cant get rid of Nketiah and Laca (covid market and great contracts Edu didnt give them). So I think you want to blame KSE (and about 5+ years of bad squad management) for not being given the green light to add another striker to the wage bill.
Tammy prefered Arsenal over Roma and delayed the Roma thing with a few days to give us a window to make it happen.