Why doesnt the netstat command display any information about ICMP connections?

Netstat will display statistics for ICMP such as Packets Sent and Received

Try netstat -s

ICMP messages arent data packets that are usable by a computers user but by the OS itself, they indicated issues with connectivity in response to requests that are being sent from the computer. For example your computer requests a web page from a particular IP address, if your router is unable to establish a connection to that it will send an ICMP message back to your computer to let it know why.

Common messages that get sent are:

Echo reply (Ping)

Echo request (Ping)

Destination Unreachable

Netstat monitors TCP\UDP ports on the computer to monitor connections to the machine, ICMP is a lower level prototcol (IP) and hence doesnt maintain connections or actively listen for ICMP packets