How is this different from someone who wants to eat bread and recite Grace after Meals with only the first blessing, instead of just not eating bread at all?

That is what I meant when I wrote that it sounds strange. First, it is pretty clear that this is the law: 1. The Mishnah in Menachot says that the tekhelet does not prevent fulfillment with the white strands, and nevertheless I would have expected them to rule that one should not put on white alone, meaning not wear a garment that creates the obligation. 2. If you were right, then even before tekhelet was rediscovered it would have been forbidden to wear a four-cornered garment.
The only question is what the explanation is (assuming tekhelet is an active obligation and not merely an existential one). In my opinion, a blessing is a permit and not a commandment, whereas tzitzit is a commandment. It is preferable to gain the commandment of the white strands even at the cost of failing to fulfill the commandment of tekhelet. Maybe one could formulate it this way: a positive commandment overrides the nullification of a positive commandment (all the more so than a prohibition).

But how do you know that an existential positive commandment overrides the nullification of an active positive commandment? That is a novelty.

First, tzitzit is an active positive commandment (conditional), not an existential one. Second, the Raavad at the beginning of the Sifra writes that an existential positive commandment overrides a prohibition.

The explanation is simple. It is not forbidden to wear a four-cornered garment without tzitzit; rather, only if he wears a four-cornered tallit is he obligated to place tzitzit on it. And if it is Sabbath, when he cannot place tzitzit on it, he does not transgress (at least on the Torah level), as explained in the Mordechai and implied by Menachot and Tosafot HaRosh on Yevamot 92; see also Shulchan Arukh, section 13, with the commentaries there. And the same applies if he has no tekhelet: he puts on white, and the Merciful One exempts one under compulsion. But all this is only when he is under compulsion; otherwise it is considered nullifying a positive commandment, whether regarding the white or the tekhelet, and certainly it is preferable not to wear it at all.

A person is allowed to bring himself into an obligation of a positive commandment even though by doing so he will end up nullifying a positive commandment under compulsion. But from here there is no proof that in order to fulfill a positive commandment that he is not yet obligated in, it is permitted to nullify a positive commandment not under compulsion.

The second formulation is more precise.

[Regarding the claim here that a conditional positive commandment (or an existential one) overrides an active positive commandment, see this responsum: https://mikyab.net/posts/73596#comment-55274 ]