I mean what is he going to do with the ship alone?
Develop it. Test it. Verify it. Perform suborbital flights.
Remember that SpaceX is also toying with the idea of offering point-to-point passenger service on Earth. (Personally, I believe that will not happen, though.)
Is it even capable of orbital flight on its own?
No, but for testing launch and landing you don't need to go to orbit.
Now the booster can be put to use immediately,
The booster can be used for exactly one thing: launch Starship. If they don't have a working Starship yet, the booster is useless.
and will probably be easier to make by far (I think)?
Yes. SpaceX have always had the maxim to tackle the hard problems first, which is another reason to focus on Starship first.
Although, seeing how much use falcon heavy has seen, I don't know about the demand about such a powerful rocket ATM, but they can at least launch big batches of StarLink satellites, I guess...
The biggest commercial use of the Starship system in the beginning will indeed be Starlink. The Starship system can launch almost seven times as many satellites per launch (400 instead of 60) as Falcon 9 can. This brings the number of launches for the planned first batch of 12000 satellites down from 200 to just 30. In total, SpaceX has just filed for another addition which (if they use everything they filed for) would bring the total number of satellites up to 42000, which would require only 105 launches on the Starship system instead of 700 on Falcon 9.
However, some commercial customers that have booked launches on Falcon Heavy have already given permission to launch on the Starship system instead, and looking further out, SpaceX will retire the whole Falcon line in favor of the Starship system. It should be cheaper since it is 100% reused and will land very close to the launch pad and not require the ASDS. (The only reason to keep the Falcon 9 for a limited amount of time would be to bridge the time where Starship is operational, but not yet human-rated, so they need to keep F9 around for Crew Dragon.)