‘Blink’ is not an inherent capability of all lights and switches. In fact, very few implement it.
The old-school way of making lights blink is to transmit a continuous stream of on/off commands, spaced about 1 second apart. For anyone with a large installation of Zigbee or Z-Wave lights and switches, this technique will flood their mesh networks with commands and acknowledgements. It’s an inefficient way of blinking many lights.
Alternately, you can use Zigbee groups (also known as scenes in other lighting technologies) to efficiently (with a single command) turn many lights on/off. However, if you have a mix of lighting technologies, including some that don’t support groups/scenes, then it becomes inefficient again.
In addition, Home Assistant does not automatically optimize lighting commands. It is unaware that you may have, for example, existing Zigbee groups so it will default to turning each individual light on/off as opposed to turning a Zigbee group on/off.
So the request for a feature to “Then blink” is an enormous challenge to implement efficiently. Plus it has to translate into a workable automation and, frankly, that’s light-years beyond what the Automation Editor is currently capable of achieving.