I don't know anything about Cord beyond this article, but my team has worked on many projects over the years where we had to add chat / commenting / notifications functionality.
I can see this being a tough market.
One - it's a crowded field, with many solutions in each of those three categories. I don't think we've actually come across Cord while evaluating solutions, which just shows how noisy it is.
Two - I struggle seeing "chat / commenting / notifications" as a unified category. Every project we've worked on had unique requirements for each of these (whether justified or not...) so every implementation ended up being different.
It's definitely a pain to roll out these features from scratch, and we always preferred using something off-the-shelf where possible.
But by the time you finish evaluating options, pick one, implement and customize it, deal with its limitations and bugs - plus projecting several years of usage costs, and uncertainty dealing with an outside vendor - I can easily see how the balance might tip to doing it in-house in many cases.
Not trying to armchair quarterback - I know how hard startups are, and respect to the Cord team for being in the trenches! Just sharing my experience.