>What if I would use a second phone, a cheap one, used only for the whatsapp (and some other essential but privacy invasive apps). I would not have that second phone always with me, but it would provide me access to the social network I need without feeling tracked or providing more data than needed.

This is what I'm doing currently: an old phone used exclusively for whatsapp (with an empty contact list); it always stays at home. I only use it to coordinate kid's stuff (school, social activities, etc), so there is no problem with me not having it with me the whole time.