What that means is, of course, increased exposure. The kids are not going to give a way their phones, they'll continue using them. When there is no wifi, they will be using the LTE or 3G or 2G networks. When the base station is further away,the phone will transmit at higher power. The phone itself is by far the dominant source of RF power to people's bodies.
Thus, ignorant parents want to decrease radiation, and the very proposals they make would increase it. Whether that really has any impact, we don't know, there's no proof, or a good theory about possible mechanisms, just speculation, mostly based on fear and suspicion.
So from the people I've known doing research and other anegdotal evidence, there is a link.
It still perplexes me how most of the studies in the end conclude there is overall no human-related high risk.
So maybe cellphones+ other generators are like peanut allergies, to some are fine, to others they are fatal.
It's too complex of a subject anyways. ... Edited for minor misspell
From 2011:
WHO: Cell phone use can increase possible cancer risk [1]
"Radiation from cell phones can possibly cause cancer, according to the World Health Organization. The agency now lists mobile phone use in the same 'carcinogenic hazard' category as lead, engine exhaust and chloroform.
"Before its announcement Tuesday, WHO had assured consumers that no adverse health effects had been established.
"A team of 31 scientists from 14 countries, including the United States, made the decision after reviewing peer-reviewed studies on cell phone safety. The team found enough evidence to categorize personal exposure as 'possibly carcinogenic to humans.'"
https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_tab...
According to Wikipedia the average cell phone TX power is 500 mW vs 200 mW for 802.11n [0]. Cell phones usually operate at lower frequency than wifi, however wifi (at 2.4Ghz) is at the same frequency as microwave ovens.
In the study the rats were exposed for 10 minutes on - 10 minutes off for 18 hours a day (at an unknown TX power), if you work in an office you are going to be exposed continuously (apart from coffee / lunch) for 9+ hours a day, and even more if you then go home and use a wifi device.
[0] https://en.wikipedia.org/wiki/DBm