Why should irelia keep her tenacity as a passive if

Irelia regardless, it would make sense for them to have tenacity. I'm all for it.

Why should irelia keep her tenacity as a passive if Singed and zac can't have it on their ults?

The problem with Tenacity on the ults of Singed and Zac wasn't tenacity being tenacity.

It's that tenacity was tacked onto both abilities completely independent of the entire purpose of using both Rs. Zac's ult is about initiating a fight and disrupting several targets in a large area-effect. Singed's ultimate is about making singed significantly stronger. Both ults still maintain their identities with or without tenacity.

However - Irelia's passive does litterally nothing besides give her tenacity. As Irelia is a fighter/assassin but lacks the same kind of 100% damage block skills as Jax, Nocturne, Fiora, Yi, Tryndamere, Poppy, Yasou, Fizz, and other such memebers of the class have - it can be surmised that Irelia's passive is specifically there to allow her to function in the large-scale battles melee DPS lack significant strategic strength in, due in large part to CC countering their DPS and reach significantly harder than CC can effect bursty and/or ranged champions.

Irelia's passive has a specific, easily understood purpose. The ults of Zac and Singed were largely convoluted and unspecific due to having Tenacity thrown in the mix with everything else.