Usually, your consent is a simple yes/no flag, no and saving that in a cookie is enough.
I have seen this “processing” before. My assumption was that it sets cookies on third parties websites instead of only the one you visit. The basis for that assumption being that some ad network and tracker websites have/offer “opt out cookies”.
I haven’t checked whether that’s actually the case.
There is no other reasonably valid explanation for it. Setting a few cookies doesn’t take that much time. It would then be either intentionally slow and lying to you, or has horrendous unacceptable implementation (which could be seen as unlikely given how obviously customer facing it is).