Indeed, this sounds quite strange if Liverpool and Arsenal are interested in signing Mbappe, but that's okay, at least this adds to the excitement about the next Mbappe's future. I think there was no other reason for Mbappe than to join Real Madrid because he really wanted to win the Champions League and the Ballon D'or, that's what motivated Mbappe if he was more interested in Spain than England. After all, Real Madrid has everything to be able to bring Mbappe as the best player in the world and he will even get the highest salary every week.
Signing a star player that every clubs also interested isn't a bad decision because it's just like investment. Mbappe have show his performance is great when he play in PSG and France national club, so it's expected there's no problem for adaption. He can give a lot contribution for the club if they really want to keep Mbappe and in the same time they can sell Mbappe to other clubs for higher price. So it's a win-win solution.