I would, but I don't need to know immediately. Plus you have the other vector of my phone sitting on a table and showing the notification to a person who can see it when they are trying to login as me.
I find it to be a poor default that sensitive data is shown on the lock screen. I change that setting as a first order of business whenever I'm setting up a new phone.
If someone texts me something that's not interesting to those MITMs but is sensitive to mom catching a glance while my phone is on the table, that's a problem this toggle creates/destroys. Threat models vary.