100,000 / (86400 * 2) = 0.58 req/sec.
I acknowledge that those requests are likely bursty, but you were complaining as if the total amount was the problem. If the instantaneous request rate is the actual problem, you should be able to throttle on that, no?
I can totally believe your site has a bunch of accidental complexity that is harder to fix than just pragmatically hassling users. But it'd be better for everyone if this were acknowledged explicitly rather than talked about as an inescapable facet of the web.