Thanks for all the support.
As an experiment on my most recent visit to central London I left the GX7 in my bag and shot with my Nexus5 instead.
I don’t have any big complaints about the results, in fact the VCSOcam app is capable of producing lovely shots, but clearly they can’t match what you would get from a proper camera. It has to be said, however, that the handling of a mobile camera leaves a lot to be desired. I can see why for casual use most people are now happy to use a mobile and to do without a camera altogether but why anyone would choose to regularly shoot street with one is beyond me. The shutter lag is truly awful, the phone is hard to hold, the focusing is slow and sometimes unreliable and there are a host of other small annoyances.
Perhaps there are less quantifiable advantages. It’s possible that I took some shots that I might not have taken with my GX7, though I’m not certain of that, and you can certainly be sneaky when shooting with a mobile because people don’t notice that you might be taking pictures… but who wants to be sneaky? I certainly don’t.
I’m sure I’ll continue to shoot with a mobile now and then to get a change of perspective but it’s hard to imagine making a habit of it.