Yes! I already use a non-privacy centric service like this, and would very much like to swap it out.
> Would you pay for it?
Yes. I'd be willing to pay $30/year for quicker updates. Maybe have a freemium model of an update per 30 mins or 60 minutes, a middle tier of 5 minute accuracy (good enough for most users) and then a premium tier of ~30s accuracy. Maybe play around with the amount of people in a group too - it makes sense to charge more if you're sharing with a small family versus a single friend.
As always with subscriptions, please make them have clear pricing, an option to pay annually (even if there's no savings) and allow auto-renew to be opt-in instead of by default.
On the monetization front, you likely can leverage the same infrastructure for an Enterprise version of the app. What many companies want is a rough geofence app that can let them know when someone is abroad for work and give them location specific information - "Oh hey, you're near the Ohio office. The alarm code is XYZ, and your badge has been given temporary access for the next 3 days."
Especially if you can assure employees that they're only giving rough location information to their employer ("Mary is in Nevada" and not "Mary is at So-and-so brothel in Las Vegas") then it feels like an acceptable tradeoff of information and benefit.