It kind of already is, but there isn't a coordinated global effort of any kind. Every GIS department has an unbelievable amount of mapping information. Because we need to, and because a lot of governments, especially in Europe, it's illegal for us to rely on google because they track too much. Some of the data is private, and rightly so, as it contains detailed private informations of properties used for internal BI. In Skanderborg Kommune of Denmark, the GIS department has even started running it's own street-view feature. But again, that's just a tiny piece of the total area of Denmark and neighboring cities might do things completely different.
We do have national initiatives like opendata.dk, that tries to extend APIs for all this data, but that's still just on a national level.
I think open street map should really be the "google maps" option exactly because it's both open and global, and I do think the public sector should put as much of it's data into it as possible, but I have no idea how we should fund it.
Grants from government bodies, with governance and stakeholders in the non-profit that operates OSM. Once that is in place, it becomes straightforward for governments and other contributors to treat OSM as the canonical Source Of GIS Truth.
We do have national initiatives like opendata.dk, that tries to extend APIs for all this data, but that's still just on a national level.
I think open street map should really be the "google maps" option exactly because it's both open and global, and I do think the public sector should put as much of it's data into it as possible, but I have no idea how we should fund it.