I actually see it the other way around: logically, public addresses are required by campaigns to fulfil the payments, but they also contribute to being less pseudo-anonymous globally. The more visible these public addresses are, the more transparent with the payments and such, but also the more information that builds around your account and that becomes of public knowledge through tracking Google Sheets, postulating post to join the campaign and so forth.
Ideally, all this should be carried out in a much more private manner which I’m sure can be thought of.
When concerning transparency you can't really have it without compromising privacy in some sort of way. However, I'm not sure how much transparency is needed when concerning the payments of the campaign. Generally, people only care about if an individual has been paid, and not how much the campaign is sending in total. So, you could potentially get users to sign up without an address, but by doing so you make it harder to prove that the campaign has sent you money, especially if you want to keep your addresses private.
I'd probably be in favour of changing the way sign ups for campaigns work, and not broadcasting your address to the world upon sign up. However, having that transparent system has worked in the past for finding cheaters of the system. So, there's definitely pros, and cons to the system. Really, the people behind the campaign should probably be on the look out for people cheating the system, and would have all the addresses. However, as the saying goes two heads is better than one, and by having the addresses public you introduce a lot more that can do the vetting for them, without needing to pay someone to do it.