Modric was one of the best midfielders in one of the best leagues in the world and even at the time everyone considered the fee that he went for to Real as a great deal. He threw a fit in 2011? 10 months later he was sold and he was coveted by many teams at the time.
Rooney as you said put in a transfer request for another reason compared to Antony altogether.
Tevez demanded a move at the end of 2010. He was brought in for British record for around 50m from memories. The next season he played like 15 games because he was suspended for his acting up against Bayern. 2012 sold to Juve for 10m or something?
Ndombele handed in two transfer request from memories. How is it going with once your record transfer nowadays?
Di Maria wanted out of United and his form dropped off a cliff as soon as that happened.
Now to the point. Antony is by far not a finished article like Kane, Modric or all of your examples. He's someone that can easily go Neres route that was sold for 15m EUR in a year time, because his form dips, doesn't want to play is a trouble in the dressing room or gets injured.
Ajax don't generate crazy amount of money playing in the Eredivisie, they are a selling club and it is what it is. Of course they are ran well and generate a profit, but it's not that easy to replace players that are hits (Antony for example) and they usually receive a lot more than they spend. Missing out on cashing in on a potential 100m asset is a very risky business considering also they are in rebuild phase this year - lost ETH along with many key players and they are far from dominant side winning the league 3 times since 2015.
So far they have started well, but this can also blow in their face pretty fast - Antony is their best player currently and clearly not happy. His value will decrease. His form might dip or play for himself or don't want to play at all. Come next year they might be without CL football (as Feyenord and PSV will probably also finish strong), without 100m offer on him to bank on with an unrest in the dressing room.
If we're talking about WC. Rafinha guaranteed a La liga transfer where he will start at the highest stage and if Antony doesn't get a transfer how will his chances improve at Ajax even if he forgets the transfer request and play well?
Your initial point was that you disagreed that players have put in transfer requests and then played well. You didn't condition that, you were just skeptical that it happened.
There have been multiple lists of exactly such players who have turned in transfer requests (whatever their reasons and whatever their ability levels may be), had their move refused and then put in an amazing season. You didn't ask whether there were players who put in transfer requests and then still performed well if they were amazing players (ie Kane /Modric/Suarez ) or weren't in exactly the same position as Anthony (Rooney/Zaha) or had a father figure manager (Vieria/Ronaldo) etc etc.
The point with Modric is that he did put in a transfer request,bad mouthed the club, went missing and then still put in an amazing season after and got his move anyway.
Tevez put in his transfer request,got rejected and then knuckled down. They won the league that season. Did something similar that next summer, played only 12 games that season, they won the league that season. Then played 34 PL games the season after, then signed for Juventus for 12 million in the final season of his contract.
From memory, Di Maria never wanted to come to Man Utd and played like it for pretty much the whole time he was here.
N'Dombele is by some distance our worst ever signing. However, he does not belong in this conversation. N'Dombele has been the same since he first arrived, lazy and failing to impress. He put in transfer request not because better clubs were in for him (if only!) but because he wasn't making it here. He was on the market last summer, where the giants of Lyon swooped in on loan....and decided not to take up their purchase option after a mediocre season. He was in the market again this summer, where again the giants of Napoli have taken him in loan, with an option for purchase. The smart money is on us unfortunately being in the same situation again next summer.
None of my comments have been about whether it's smart for Ajax to turn down such a bid (it's clearly an absolutely insane bid). It's been about the pervasive attitude on here by some that if someone is turned down for a transfer request, they just give up and down tools, despite multiple cases to the contrary. Ajax are still a selling club, in fact they sold a player to you literally this window.
If he doesn't get his move and then just gives up and lets his career go the way of Berahino (a player who did let the failure of his transfer affect his future career), he's going to be the party most affected. Not Ajax and not Man Utd. He'd do well to remember that. Carry on, put in another good season and he'll get his move.