Chelsea requested a loan for Osimehn with a buy option due to the signing of new striker Marc Guíu from Barcelona. Management may have preferred not to have two strikers on a permanent deal. However, I believe Osimehn prefers PSG over Chelsea because the English team does not know how to keep a player, they normally sell a player who does not perform as expected in his first season, while PSG dropped out of the race for Osimehn because of the high price and the players' refuse to reduce his salary. Arsenal can do better next season, but as you mentioned, they still need another striker to avoid repeating last season's mistakes. Arsenal had a goal differential advantage over Manchester City last season, but their performance declined with time, and Manchester City finished the season with the same goal as Arsenal. So Arsenal deserved a striker capable of scoring constantly to compete with Manchester City.
Honestly, I'm tired of the back and forth; whoever can take him should but the question will be, can he able to fit in at the club he finds himself?