There are significant differences between the 3 clubs & acadamies you listed. For the majority of youth players, the pinnacle is the first team if you begin as a child - even more so if you are local to the club (esp. Catalan). In the case of Ajax, currently the 1st team is not considered the pinnacle in European football so the aspiration for a player is often to eventually depart as has often been the case with Ajax players. In the case of City, I can only think of Foden as an example - they are not Barca in this regard despite the best efforts of former Barca players/execs/coaches to change the culture of the club.
Barca, on the other hand, is typically the pinnacle for a youth player and a departure ahead of the 1st team is typically down to a few scenarios.
1) Player simply is not at an appropriate level for the 1st team of Barca
2) Player is appropriate for 1st team but due to squad depth will never play or find it difficult to find minutes. Often leads to loans or transfers with buybacks
3) Player is not a priority due to discipline (Not common) or attitude/professionalism (Latter was levied at Deulofeu, for example)
4) Player or cantera players in general not a priority over market transfers, aka galacticos - this happened with Gaspart and worse for many cules under Bartomeu & Rosell now (Only Sergi Roberto had been promoted & remained w/ the first team in a decade)
Otherwise, cantera players desire to succeed here. Eric's departure underscored Points #2 & #4 with the latter being a larger problem over the last decade - the erosion of La Masia and failure to integrate youth players from the Cruyff model of development (With it's Ajax roots)
Look at Puig, he refused to be loaned out or transferred - he insisted on getting a 1st team shot and was content to even stay with the B team until he got the chance. Alena went through similar and was effectively forced out as was Carles Perez and Munir before him.
You are right that there needs to be a correction at Barca but the huge problem at Barca currently has been Rosell & Bartomeu and their dismantling of the cantera as a fundamental bedrock of the club & it's playing philosophy. Even at youth level, the club still does excellent until that 17-19 year age group of Barca B - primarily because they abandoned their playing style & instead recruited from outside the club rather than trust the kids nevermind promote them. Ergo, many sought to leave rather than be treated like cattle
Broad generalization without understanding the nuances of the cases of Cesc & Pique which occurred during the transition to Laporta after Gaspart - there was a lack of confidence or trust in La Masia and those talented players sought opportunities elsewhere as a result. Pep had just left as a player and even Xavi considered leaving due to that abandoning of Cruyff principles. When the club course corrected under Laporta & eventually Pep, they returned and after that no other cantera player left the club who was prioritized - until Rosell was elected in 2010. Thiago was almost immediately sold a year later. Their model was to use the cantera players as commodities and it underscut that aspiration to thrive at the club
Only hype had anything to do with Gai Assulin, he was never in the bracket of breakout stars - he was a one trick pony with pace. Bojan had a great start but when he refused Pep's advice to develop at Barca B he was marginalized - look where his career went. Personally, I liked Bojan but he had a confidence/mental issue - it was easier for him when he was a substitute and not seen as a protagonist. Again, apples & oranges comparisons
I'd say a player like Lee Seung Woo is a better example of what you describe, a phenom until he hit 15/16 and his progress slowed incredibly until he was sold. I was convinced he would be a star like Kubo (Before the FIFA ban). Some are not aware but like the 2002 golden generation of La Masia talents, Ansu, Kubo & Garcia formed a more recent golden generation that was believed to be nearly as great. Only luck allowed Ansu to get his chance since Suarez was recovering from injury in summer along with Dembele. Kubo was rebuffed on his desire to return and ended up at RM while Garcia headed for the exit 3 years ago - again due to lack of faith in sporting direction of the board
Cesc, Pique & Messi were part of the 2002 La Masia generation that were the most dominating youth side the club has known. Even before Cesc was poached by Arsenal, he was the voted the best player (Golden Ball & Golden Shoe) at the FIFA U17 championships. Let's not try to revise history, him & Pique were destined for great futures. They simply lacked confidence in the direction of the board, not unlike today where many super talented players have left (Olmo, Adama, Deulofeu, Munir, Thiago, Abel, Grimaldo, Cucurella, Perez). Hopefully under a new board, the club will course correct as I see the cantera as fundamental to the success of the club
As for Garcia's immediate future, more links to the club prioritizing him - whether that is true or a smokescreen to appease the base difficult to say still
