Note: answer based only on docs, I didn't play with docker much.

If you choose scripting you could pick a higher layer than just ps, based on either:

• the docker-compose events CLI:

Usage: events [options] [SERVICE...]

Options:
    --json      Output events as a stream of json objects

Stream container events for every container in the project.

• the docker events CLI:

Description

Get real time events from the server

You'd be looking for the die event of the container(from Extended description):

Use docker events to get real-time events from the server. These events differ per Docker object type.

Object types

CONTAINERS

• die

The event appears to be generated regardless of the restart policy (from Docker Events Explained):

But you're right, there's a ton of monitoring tools out there, I also suspect some already do what you're seeking.

Note: answer based only on docs, I didn't play with docker much.

If you choose scripting you could pick a higher layer than just ps, based on either:

• the docker-compose events CLI:

Usage: events [options] [SERVICE...]

Options:
    --json      Output events as a stream of json objects

Stream container events for every container in the project.

• the docker events CLI:

Description

Get real time events from the server

You'd be looking for the die event of the container(from Extended description):

Use docker events to get real-time events from the server. These events differ per Docker object type.

Object types

CONTAINERS

• die

The event appears to be generated regardless of the restart policy (from Docker Events Explained):

But you're right, there's a ton of monitoring tools out there, I also suspect some already do what you're seeking.

Just aimlessly wandering through those links I got to Implementing Docker event monitoring from scratch:

What else? I can create alerts on them. The next time any of my containers decide to puke and die, I can get an SMS message about their doomed state.