Just as you have said Arda Guìeŕ situation at Real Madrid is indeed challenging given the stiff competition for this position, with top player vying for the same spot well if you check it is to tough for him to get sufficient playing time, a loan could be beneficial for hims growth allowing him to gain more experience and minute on the pitch. To me his development is crucial at this stage in his career and a loan move could be perfect solution this would enabled him to play regularly and also gain some confidence and eventually return to Real Madrid as a stronger, and more experience player.
that's right, it's understandable that Arda Guler should request to be loaned to another club, so that his talent can develop better. There's almost no room for Arda Guler to become a key player in Real Madrid main squad, and Ancelotti can't offer many playing opportunities because there are still better rotation options. Serie A could be a suitable choice for Arda Guler, but if he wants a more difficult challenge, then the Premier League is the right choice. I hope he takes that opportunity next season.