Oh this is the main task of Real, to sign as many players as possible as free agents, it seems that they liked it after they did it with Mbappe. It is not known whether they managed to do it with Alexander-Arnold but they really wanted it, now they are trying to do the same with Kimmich, for them it is a good strategy, but those teams that lose these players also lose a lot of transfer money.
Although it is not a fancy thing to do and rather a painful way to do it but I can say that those clubs you mentioned have definitely got no right to complain when a player makes this decisions. First of all I don’t get why a club like Liverpool who know Arnold has great potential and they value him so high will actually not negotiate his contract extension since when it has like a year left to expire, this is the reason why you use clubs put this clauses of extending with year after the main year is over. Liverpool left such players to the dying time which will definitely make them to have more upper hand in the negotiations and that’s why these players are demanding just way too much.
Moreover Just like Real Madrid did to PSG they offered the club money season before the players contract expired but the club went ahead and did the other way around, same thing Real Madrid did with Arnold yet again even though I can say yes it was actually not a good or reasonable amount but it is a good way to start. Look at how Lille actually fought their way with this Leny Yoro situation and got Manchester United to sign him because they knew the player will be leaving for free the following season after Real Madrid had tried their antics.
This Kimmich situation though has been different to the others, Bayern Munich have actually in the last two summer be throwing him around to even clubs like Barcelona and the rest they already had him out of their plans when Tuchel arrived and the player fell out with him. He only got redemption when the player had an excellent Euros with Germany and through the arrival of a new coaching staff. So I wouldn’t bash him if he still wants out from here after they had actually put him out on sale before.