for precisely the same reasons people run lottery syndicates.

problem is, in a lottery syndicate, obviously you will know who paid into the ticket fund and who didn't.

How do you plan to verify someone in the syndicate is actually trying to solve blocks?

The best way I can think of is by measuring their average number of hashes per second and then have a secondary target their client must achieve which acts as a proof of work for the syndicate to know that this person is dedicating their CPU resources to generation.