2qwerty
“Ok so if this blue ink happens to be the real techailes are we fine with being mevatel a mitzvah?”
I wouldnt say “fine” We daven multple times daily for the return of many mitzvos that we dont fullfil lfor one reason or other.
“And if its just ink what did you lose by wearing it just for 10 mins a day in the privacy of your home?”
A few things.
1. Who says I dont
2 I have no problem with putting it on privately, my concern is the mass communal efforts. Many Rabbonim as pointed out did put it on, though they did not advocate for others to put it on. (I dont fully understand the reasoing of these Rabbonim, the ones of asked told me a combination of yehura and breach in mesora that they felt they avoided by doing it privatly liek you suggest as opposed to mass communal effort)
3. there may be an issue of different color tzitzis than beged.
4. that isnt how halacha works. Say there is a treifa that has a 10% prevalence in cows. The Halcah is thsi is a miut sheino matzi and we dont check. That means (statistically) if you eat meat from 10 different cows you ate meat that had a treifa. What is the harm in just avoiding meat or checking?
That isnt how halacha works. There are rules, and if you can eat meat without checking then you can eat it.
If Techeiles requires a MEsora, or if there are sufficient questions on it we dont need to do it just in case, (especially given the cost)