As Beri said, only 1 naturalized player can play at any one time, so even if they naturalize 100 players, it won't technically get them any closer to trophies than if they were to naturalize 1. However, I think it's demeaning to players themselves (at least those that are hoping to play for the NT). Okay, so you have a rotating stable of half a dozen hopefuls. You try one of them at VNL at such and such a year. They play...fine. Nothing spectacular, but not bad. You tell them: "Okay, get back to your corner. You there, you're next." You try the next one in the rotation at the European Championship later in the year. And so on and so on. There is something... inherently demeaning and humiliating in the whole affair.
And what happens when you introduce an overwhelming element, like for instance (as 7up said), Egonu. Say, TVF decides to say to Egonu: "Okay, you have problems with racists in your country. You love your country, but it's clear not whole of it loves you back. And your generation isn't as overwhelmingly superior as many have expected and predicted. So, we'll pay you 10 million euros to not play internationally for the next 2 years. You apply to change your sport citizenship and after a waiting period, you play with us. You'll still be young enough to compete for years with us, you'll be showered with love and adoration and you'll earn significantly more money".
Vargas and Alexia (and any other player that Turkey might wish to naturalize or any player who wishes, for whatever reason, to play for Turkey) can never hope to compete with her. They have been looking forward to the day when they are going to try on that jersey that they might have been dreaming about for some time. They maybe experienced critiques and blowback from their home countries. But it's okay, it will all be worth it at the end of the line!
Now, you are basically telling them that this is the end of their aspirations. Once Egonu is eligible to play, no other player in the rotating stable will ever be invited. And why not do it? If we are accumulating assets for future deployment, why not go for the ultimate prize? Might as well...