Why does it have to be a mosfet? A constant current generator can, in my humble opinion, be implemented quite as well with a transistor.

Yes, of course! The idea of using the MOSFET is to save current. With a bipolar transistor you would need two currents, one to flow through opto and one to make the current source work. With the MOSFET you need only one current. The same current which is flowing through opto is used to make the current source work.

But, of course, if one uses your idea with this strobing of current source even a standard design using biploar transistor will work.

Kai