Yes! I too would love to see the API return reply count in a similar manner to favourite_count and retweet_count.
Currently we have to loop through tweets with the same reply_to ID which in many cases is not feasible and will soon hit rate limits, as well as creating unnecessary lookups
This would be useful to so many 3rd party Twitter apps, as number of replies is a good indicator of engagement and could encourage users to converse if they can more easily see active conversations. My https://socialbearing.com/ site for example allows tweet search results to be ordered and filtered by number of retweets and favourites. I would love to be able to add replies (just a basic count) to the site 
If the Twitter UI and app now have a way of easily displaying reply count, I would hope it should be possible to make available via API
Thanks