Indeed. ~2m is the limit of accuracy for a typical smartphone GPS - I've gotten down to 1.3m when standing in an open area for >10 minutes with 12 satellites in view, but that's an exceptional case.
In practice, accuracy will be in the 5-10m range.
It doesn't make it any less creepy though... which then begs the question of how the number of people wanting to send their location would change with how "approximate" of a location (i.e. rounding to some radius) they're sending. Nearest 100m? 500m? 10km? 100km? State? Country? Continent? ... Planet? I would probably be fine with the last one, but no more than that for anyone I don't know well.
My phone – which combines GPS with GLONASS – usually gets about 40m accuracy with just GPS, but with combined GPS and GLONASS I have about 24 satellites in view, even in buildings, getting better than 1m precision.
Precision is not the same as accuracy. Although the reported values may have 5 decimal places of precision, I find my location is often a bit off.