I agree 100% and have been agreeing with anyone who brings it up for almost 2 years now.
Is that a typo you ask? Why thanks for asking. No, it's not.
Chat has been thoroughly updated just one time since the inception of DS and that was July 2016, with a teeny little patch in August 2016. So we're at 1 year 10 months later with no improvements. This is a very social game and the chat interface leaves much to be desired. The most requested thing by far is the ability to delete old chats.
Go here to see what I mean.
Back in February 2017 (for those of you who hate math, that was 1 year 4 months ago) I made this thread with lots of links to other threads asking for same things. I won't update it because, well, there's just so many more that have come along since then. Using the awesome search function will get you to even newer threads with the same basic content. But I can also save you that time with a deeply thought out and well researched summary highlighting well over 100 posts:
We want the ability to delete old chats!
When will be able to delete old chats?
Please, oh please, update chat!!
Chat needs an update!!!