Thanks for raising these concerns.
Despite having studied physics (inverse-square law) and electrical engineering (though I wasn't the best student), I am concerned by how readily and glibly folks dismiss concerns about possible health effects of EMFs. The fact is, there's a lot we don't know about our own biology, and heating effects and ionizing radiation aren't necessarily the only possible modes by which EMFs could harm us.
This documentary, while suffering from some poor production values, presents the hypothesis of some researchers (whose CVs I have not examined) that round-the-clock EMF exposure reduces the body's natural production of melatonin, a potent anti-oxidant and regulatory hormone, since the body doesn't distinguish between visible light and RF radiation. This reduced melatonin production allegedly can lead to a reduction in the body's ability to fight cancer growth.
Time will tell but, as you say, we're performing a large-scale experiment on ourselves.