No, simplifying their links would work. Use an url shortener, e.g. https://business-name.mailchimp.com/campaign-name-abc123.
The only advantage that routing clicks through MailChimp has, is clicktracking. Clicktracking can easily - trivially - be handled serverside. Just embed per-recipient unique ids in the url.
If MC is worried about customers lying about #clicks, they coukd easily make all urls point to A.com/mailchimp?mailid=xxx&linknum=yyy.
That forces A.com to run the one thing MC sends them to sort out the clicks... which of course does the clicktracking and hides the useful info from their customers.
The processing power would still be needed on mailchimp's side. All the customer (A.com) does, is add a tiny redirecting script on their site.
It's similar to how one fingerprinter for android works.Get your client to forward you the user details. User only sees the client (so nothing suspicious, no 3rd party to be blocked), while encryption ensures that your client has to forward you the data - they cannot parse it themselves.
Case in point: google.com
The real reason they don't do this is because it's a more involved set-up from the customer's side. As people mentioned, enterprise-oriented mail services will do this kind of thing but MailChimp is a long tail solution.