Why don't computers have "computer-numbers" equivalent to phone numbers

Why doesn't every computer have 256 char domain name, along with a private key to prove it is the sole owner of the address?

Edits: For those technically inclined: Stuff like DHCP seems unnecessary if every device has a serial number based address that's known not to collide. It seems way more simple and faster than leasing dynamic addresses. On top of that with VOIP I can get phone calls even without cell service, even behind a NAT. Why is the network designed in such a way where that is possible, but I can't buy a static address that will persist across networks endpoint changes (e.g. laptop connecting to a new unconfigured wifi connection) such that I can initiate a connection to my laptop while it is behind a NAT.

• Yes, it would be a privacy nightmare, I want to know why it didnt turn out that way
• When I say phone number, I mean including area/country code
• AFAIK IP addresses (even static public ones) are not equivlent to phone numbers. I don't get a new phone number every time I connect to a new cell tower. Even if a static IP is assigned to a device, my understanding is that connecting the device to a new uncontrolled WiFi, especially a router with a NAT, will make it so that people who try to connect to the static IP will simply fail.
• No, MAC addresses are not equivalent phone numbers. 1. Phone numbers have one unique owner, MAC addresses can have many owners because they can be changed at any time to any thing on most laptops. 2. A message can't be sent directly to a MAC address in the same way as a phone number
• Yes, IMEI is unique, but my laptop doesn't have one and even if it did its not the same as an eSim or sim card. We can send a message to an activated Sim, we can't send a message to an IMEI or serial number