AGPS actually means two different things.
If by AGPS you are referring to the use of nearby WiFi and cellular networks and querying a service for that (there are ways to have that info purely offline, but I do believe such databases rely on many people leaking their positions to exist at all), I'm not convinced your approach helps much:
1) if you run stock iOS or Android with the Google services, I believe you are already screwed anyway: I wouldn't trust them not to constantly leak stuff about you in the background even if you don't actively use the GPS, at least to build their traffic info and to keep their access network-based location database updated. If you are concerned about the privacy aspect of this stuff, you should be getting rid of the Google services anyway. That leads to the next case:
2) If you are running a phone without the Google services, then you don't have that kind of AGPS. Unless you go the extra mile of explicitly configuring microG to enable network-based location. I used to do this, but on my current phone, getting the position purely from GPS has been so reliable and quick that I didn't bother setting this up (I suppose it could provide some battery saving, but there are privacy concerns indeed, and not relying on such databases that basically depend on people giving up bits of their privacy is always nice). Your main concern there would be the shady blobs most phones run that could be doing you don't know what behind your back, but that's regardless how you use your phone.
If by AGPS you mean the download of the data about the positions of the GPS satellites (MSA) then yes, indeed, I agree, you will leak to your service provider (but not more than if you are not already fully offline - so basically if you use your phone like a phone you already leak as much) and to the server providing the data (which is probably Qualcomm (XTRA) or Google, or possibly your service provider). Then the solution is fully offline, and your current options are non assisted GPS, which can take 10 minutes in good conditions to get a fix if you haven't used it in a while, and reading the map. From what I understand, your current strategy is to help with the latter, which needs to be better than eventually getting a GPS fix (which feels somewhat niche, but I can see some advantages).
(There's also AGPS MSB where you basically ask a remote server to compute your location from what your GPS receiver gets and nearby cellular networks, the leak here is obvious but from what I've read this is quite rare nowadays, it was more useful when GPS receivers didn't have enough compute power to do the compilations themselves, so that would be mostly irrelevant.)
All in all, if I'm not wrong (happy to be proven wrong): as far as privacy is a concern, depending on what you mean by AGPS, your approach only applies to, respectively, devices without the Google Play Services or similar stuff, or to fully offline devices. It needs to be better than, respectively, GPS assisted with the satelite positioning data (which can be good for up to 7 days and then updated through regular GPS if I'm not wrong), or regular GPS. I believe your angle of attack can be battery usage, or better than the time to get a GPS fix. That seems quite tough especially that your approach as I understand it is intrinsically scoped (works mostly in cities where it's easy to ask about what's around).
I believe a stronger angle of your approach is resilience: less dependency on the GPS system which can indeed be jammed or which can fail (although there's redundancy: we do have several constellations of satellites from different countries, so a general failure seems unlikely, and a GPS failure would be catastrophic because many critical things depend on it).
Now, there are devices or places (especially in dense cities with high buildings) where the GPS simply doesn't work well, so a convenient, privacy-preserving alternatives to the GPS would be great in those situations6!