Edit: correcting a typo
The pitch for in-orbit refuelling is clear. Less clear is the advantage of a tank in (a close, but wrong) orbit over one on the ground with a launch booked.
Rockets become more efficient as they get larger, you get lower structure to payload weight ratios and you suffer fewer losses to drag in the atmosphere. The same scaling goes for your fuel tanks. You want to get the biggest fuel tank you can in orbit and then use efficient ion engines to move for whatever delta-V corrections you need.
Doing some back of the envelope calculations, a single 20,000 kg depot could provide fuel at approximately 10% of the cost of individual launches even with an extraordinarily inefficient 300 m/s of delta-V change for every refueling. Realistically you could probably get under 1% with efficient planning.
Kind of like remaking the old hub and spoke model, with Starship being the bulk 747, similar to the era when air travel was prohibitively expensive and demand was still too low to support direct point to point everywhere.
This depot is in a sun-synchronous orbit. There are a ton of long-term, extremely expensive, Earth-observing satellites between 600 and 800 km with inclinations of 98 degrees in this area. Yes, it's a large volume of space, and yes, it's not like you can just point yourself at another satellite, fire a thruster, and coast over to it, but if you could extend the lifetime of your billion-dollar meteorological satellite for a few million you might want to have this thing fly over to refuel you.
I doubt that they'll be moving massive satellites with huge telescopes, radars, communication dishes, and solar arrays to the tanker, rather, they'll fly the tanker to the satellites.