If they were made to donate anonymously they wouldn’t donate at all.. At least not legally.
See, you're a quick study! I believe that Rush used to call it "Defunding the left". A few news shots of the illegal donors and recipients being perpwalked to police vehicles would greatly discourage the rest. Lobbyists could still lobby, but not on the basis of "we gave you X, now you give us Y". They'd have to demonstrate that the policy they are pushing would benefit the people, who would benefit most and what potential harm it could do and to whom.
Take the money out and much of the corruption goes away. Some will cheat, and when caught will be punished by ending up impoverished.
The only way any of this happens is if we the people demand it overwhelmingly. Sad to say, unlikely to happen.