Real Madrid has too many good players played in Arda's position, and makes him unable to compete. It's why i think let him leave as a loan is best decision. He gets a lot of advantage, and his club is also able in signing a new back to strengthen their squad.
I don't see negativity in this case. It's all good for his future, and he clearly must get more minutes in order to develop himself better. It's better rather than see him warmed bench, and has no use to the club.
Arda need to wait until the senior player gone and this might not happen in near future.
Unless there's a team want to buy out Rodrygo with an insane fees, there's no way for Real Madrid to sell Vinicius or Mbappe.
Premier League is the most competitive team too, if he play for Bournemouth, he will know the struggle to play in mediocre team, which could force him to improve. This also make him able to appreciate Real Madrid, since in Real Madrid all of the players are high quality.
The main question is how long? There's no guarantee if Madrid won't sign new player at his position in the future. That's why i think loaning him must be the best decision.
They have to go to the premier league, or their career will stuck. This is dilemma considering they leave from high tier club to play in the mid tier club, but as long as it's still remain at the competitive league. That's fine.
The best decision arda guler can make for himself and his development is for him to go out on loan to a team that is going to be playing him regularly for like two seasons, and just as you have rightfully pointed out, he needs to come to a competitive league like the English premier league where the competition will be fierce, because it's going to aid his development faster, than going to a lower team in the Spanish laliga or a more inferior league.
So if he can stay out on loan for two seasons, and the club he went to plays him regularly, he is going to improve massively, and when he is back to this real Madrid team, he will be able to dislodge one of this top stars in this real Madrid team if only he is in a better form than them, so staying put at real Madrid and be hoping to get a chance is what he wouldn't be given for free, he must earn it, and the only way he will earn his place in this real Madrid team is by going out on loan for two years, when he is back after then, I believe that he will be mature enough to compete for a place with this too guys benching him right now.