From the context of your previous comments, it seemed like you were talking not about not having a mobile phone in general, but rather a SIMless phone. Using it over Wi-Fi only is indeed doable - but you'd need an Airplane Mode on an OS you can trust, just having no SIM would not be enough.
Also no, I did not have such a job - I don't understand how this question relates to the conversation.
I wouldn't trust them not to store the initial one as well tbh. Nothing technically stops that and it's in their interests.