It's highly imprecise, but not impossible. The alerts are already "this is over some threshold of ground acceleration", so there's an inherent severity estimate in the alert going out at all.
But expected intensity information isn't included because:
1) it's still a very imprecise estimate at that time,
2) actual intensity of ground motion (what you care about) will vary dramatically by location, and
3) people don't deal well with that kind of information in an alert that is really meant to be "hey, take cover".
When I was working in SF (Near Montgomery BART), there was an earthquake, but I was at the dentist at the time. The dentist was nearby on a hill near Union Square. The earthquake was not felt at all there, but it was apparently rather strong at the office down the hill.
We have a demonstration that it is possible just today, as the people who got an alert also got an estimate of the strength. The broadcast estimates were slightly low: 4.8 for a 5.1. But in the neighborhood.
I got a notification (in Santa Cruz) that mentioned a magnitude (4.9), a distance (~30 miles), and that I should expect mild shaking. I saw the notification a few seconds after it arrived, because my phone was making a weird noise, and the shaking started immediately after I read the notification. It was probably the strongest earthquake I have experienced in the ~5 years here, but there were several similar earthquakes every year when I was living in Chile.
If you send notifications for minor earthquakes like this, an estimate of the intensity is mandatory. At least in countries like Chile (and Japan?) where earthquakes are common. Otherwise people will learn to ignore them as false alarms.
I'm thinking the best thing to do is threshold the notifications to ~5 or above, so they're worth paying attention to, and a certain distance of course. Not an expert though. 5 is major enough to want to know isn't it?
I'd also say the average person has no intuitive sense for earthquake magnitudes and giving a somewhat precise number wouldn't affect their behavior the way a broad category warning like mild, moderate, severe, and catastrophic would.
I suppose the people getting these notifications really just want to know if they should scramble for safety immediately.