100% this.In my personal experience sometimes I mentally can't respond to messages, even to say 'sorry I cant talk atm' 'cause it does use a lot of mental energy.
This day and age people send messages and expect instant replies but you shouldn't have to be constantly in demand even if it is showing you online.
If you need a reply urgently try contacting the person another way or just send another message saying you need a reply.
I don't like the idea of being available on demand. Like others have said, the very concept of it is invasive, strange, and well... demanding.
Escaping/Switching off is a necessity, especially in the modern world. We all need dull, non-alert down time. Browsing the internet, and watching movies are my escape, for example. Reading and responding to messages requires attention, alertness, thoughtfulness, and the anticipation of a continued conversation. Sometimes I just don't have the energy and desire at that moment to engage. I read the message because I always check and clear off my notifications, but I just don't feel like engaging for no other reason other than I don't feel like it right at that moment. Never anything personal.