COI allows everyone to chat on basis of the current email infrastructure, the experience gets better with a COI compatible client and even better with a COI compliant server.
We have launched "Trusted Email Services", TESMail.org to describe a secure email setup. All encryption / security / filtering mechanisms that are available for email are available for COI. In addition users can use client-supported GPG-based encryption, possibly facilitated by initiatives like autocrypt.org and cool clients that will provide it. With COI enabled servers there will be more alternatives, when messages are being sent directly from COI server to COI server, along the lines of what the current messenger silos do, only open 
COI is an extension to the email protocols, COI does not "add another one". COI is designed with full backwards compatibility in mind, so that anyone with an email address can participate in the communication. The experience is only improved by using a COI compatible client and potentially selecting COI supporting service provider / email server software. Email is a federated, established and world's largest messaging environment - there are 7 billion active email accounts. You can also host your own email service - even when you are not a technician, you can use solutions like https://thehelm.com/.
IMAP and SMTP are the most ubiquitous message technologies, so it makes sense to base COI on that. JMAP provides alternate means to talk to the email backend, that is very (mobile) client friendly and brings in contacts and calendar. Very cool! We hope JMAP will pull in the enhancements COI provides as well.
Dovecot is working on becoming COI compliant and we hope to share developer previews soon. At the same time we are working on the server specification drafts and cooperate with bodies such as the IETF.
COI is complementary to Matrix. And XMPP for that matter. We do not try to replace any of them. COI has the advantage of global distribution and ubiquity. We believe this network effect is necessary to replace the silos.
In theory Matrix provides the option to communicate with email recipients via an email bridge. However, COI is built on email and does not need a gateway or any translation, COI messages are email messages, thus avoiding any gateways, transcoding etc., which usually means asking for trouble.
We are currently reworking the client specification draft and will publish the next draft on GitHub soon.
You don't need to switch. From a COI client you can communicate with any active email account (btw, 7 billion worldwide!). COI clients will enhance the email experience in various ways, we expect the following reasons to be the main drivers for adoption: