Brilliant idea... the "right to be forgotten" has been a hot topic in various ways, and I would expect with EU privacy regulations and using Google products, this should be a significant consideration.
It's one thing to lookup a known callsign, but in the process others' callsigns appear, which leads to personally identifiable information and potentially crimes of opportunity.
For example, bad guy sees an APRS object near them, looks up the callsign, sees the ham's info on
QRZ.COM or elsewhere, "hmmm, nice truck, lots of gear and tools, and it's just around the corner..."
Yes, we all understand if you don't want to be found, don't holler or light up. This could be an interesting discussion, and desirable feature.