This leaves such a poor taste in my mouth. Perhaps the proper UX is to then _not display comment counts_ if your performance/cost tradeoff has determined that you can't display comment counts accurately. For higher comment counts it might be fine where a user isn't expected to read all 5000 replies(ignoring the edge case where its 5000 private/blocked accounts replying), but if a tweet has 2 replies then the user who clicks it expects to see those.
Other large platforms have been able to solve this issue either in UX or implementation, so "web scale" isn't a good excuse.