It's actually the other way around. There's no such thing as globular maps. Any globes you see are simply globular projections of a flat earth.
If I say, each and every accurate map is a globular map, how do we solve this disagreement?
Evidence? I see overwhelming evidence on the globe side.
All maps in use for navigation are build on
spherical coordinates. On the vast majority of these maps you can derive spherical coordinates directly, others mostly include an advice how to transpose coordinates, for others general advice is available.
Each and every day millions of car drivers, navigators on ships and planes, even cyclists, hikers and explorers verify distances and directions with their odometers and compasses. I never noticed any frequent complaints about inaccurate maps.
There's not only one mapping service producing maps, don't know how many in total, but never heard about any significant inconsistencies between maps from chart service 'A' compared with chart service 'B' (if any, than it's about some details missing). I myself concurrently used sea charts from different chart services, found no issues.
And now the best:
OpenstreetmapThat's an open source crowd workers project. Over 1 million contributers are registered now. Additional contributions from a vast number of geolocation services, donations from many - also governmental - organizations are put together in one global (!) mapping database. All fits together with no significant issues. Myriads of maps are produced from the data and thus verified by millions of users of these maps.