I agree that we should see the comment count on the search screen, but for a different purpose than just 'seeing activity on a question'. Comments aren't great things to have lots of. I'd like to see comment counts to know that I might need to extract vital info out of them, and edit that information into the post proper.
The Stack Exchange commenting system is meant for clarification of the question/answer and not extended discussion. By design, comments don't have revision history, nor are they backed up - should they be removed they are lost forever.
Thus, wherever possible we should be:
- Editing vital information (system specs etc) into the question
- Prompt an Answerer to edit information back into the answer
- If the question is 'answered' in the comments, prompt relevant parties to add it as an answer
The only thing I would add to this feature request is: Change the text colour for the comments count, with higher number of comments displaying in deeper shades of red. That way, it will become very obvious which questions have too many comments.