Another possible reason why I think Atletic decide to continue being loaned Joao Felix to different clubs is the financial benefit that Atletico Madrid gains from these deals. For instance, in the transfer deal with Chelsea for just half a season, Atletico earned a significant amount of $16 million without having to give anything in return. If this was only for a partial season, one can imagine the potential earnings from a complete season deal.
It's pretty obvious you've not been following the Spanish La Liga. Spain has a very strict financial policy that makes it difficult for teams to hold on to highly paid players except the club is generating a lot of money.
There's a reason Barcelona had to activate leavers before they could sign players next season. There's a reason Sevilla couldn't buy a valued player during the summer transfer window. There's a reason a lot of Spanish teams let their top players leave recently, an example is in Isak that left Real Sociedad to Newcastle. It wasn't because he was not good, but an offer came and it was an offer they can't refused because of how strict the rules are and they could use that money to loosen themselves a bit.
To me, Felix is not as good as he is rated, but he is good. Atletico are not selling him because he's not good, but they need space in their wage bill snd they need to sell a big player to balance the financial books or else they will be sanctioned by La Liga.
There was even a time they considered selling Rodrigo De Paul just after his first season. It had nothing to with his abilities.
Barcelona right now are fighting for a way to bring in new recruitment without letting go of their high profile players.