Tzitzit with/with out Techelet

I understand that the Mitzva of Tzitzit means "with Techelet". Thus, wearing Tzitzit without Techelet is wearing a four cornered garment without Tzitzit - which is worse than not wearing a 4 cornered garment at all. My question is - is Techelet integral to the Mitzva or just an addition (Hidur) to the Mitzva? If it is the former, why are we allowed to wear Tzitzit without Techhelet? and surely we should now start using what many assume is authentic Techelet - even if it is a Safek.

The Rambam [Tzitzit 1:4] states that Tchelet and white are not essential in order to fulfil the Mitzvah of Tzitzit. If you have Tchelet you wear it with the white and if not you wear the white only [like most people wear today]. However this does not mean that they are two separate Mitzvot [ibid 5] I agree that it makes Halachic sense to wear the Tchelet of the Ptil Tchelet Association and I personally do so as well, nonetheless some of the prominent Poskim of our and previous generations do not recommend until will be proven without any doubt.