Yes, there's a default app to handle SMS. And Google would like you to use Google Messages for that, which is inherently non-private because SMS (and RCS) aren't private.
but there's nothing about SMS that makes it a default other than it's what most people use. You have to open an app to send a message, there's no default way of sending a message where you aren't choosing an app first, and if you want something private and secure, you can choose something other than SMS.
I think by 'default' I meant on the home screen of apps on a factory-new Android phone, presumably one messenger app is pre-installed and on that list. Perhaps, even configured as part of a phone onboarding experience.
This must be the disconnect. As an Android user, it wouldn't occur to me that the "default" messaging app (usually something barebones and ugly) would influence how I send my messages. I just use whatever app I want, SMS or not. But unlike Android, Apple managed to popularize its own all-in-one messaging solution and in so doing brought encryption to more conversations. Google could try to do something like that with Android, but thus far they've simply remained agnostic.
It is usually a SMS-based app but it is not the same one for all factory-new Android phones. Some manufacturers will ship with Google Messages and some such as Samsung have their own messaging apps which will be the default in most but not all cases. If purchased through a carrier sometimes the default app will be the carrier's messaging app even if the phone manufacturer has their own.
but there's nothing about SMS that makes it a default other than it's what most people use. You have to open an app to send a message, there's no default way of sending a message where you aren't choosing an app first, and if you want something private and secure, you can choose something other than SMS.