`docker save` does not download image like `docker run` if it isn't already stored locally

Description

docker run ... pulls an image down if it does not exist locally, however, docker save does not automatically download the image if it does not exist. For consistency, docker save should probably also automatically download the image if it's not present locally, the same way docker run does.

Steps to reproduce the issue:

1. Remove an example image locally
2. Attempt to save the image via docker save -o outputfile path/to/image:version
3. Witness error that the image does not exist.

Describe the results you received:
docker save -o failed if the image wasn't already stored locally.

Describe the results you expected:
docker save -o should have downloaded the image if it weren't stored locally.

Additional information you deem important (e.g. issue happens only occasionally):

Output of docker version:

Docker version 20.10.6, build 370c289

Output of docker info:

Client:
 Context:    default
 Debug Mode: false
 Plugins:
  app: Docker App (Docker Inc., v0.9.1-beta3)
  buildx: Build with BuildKit (Docker Inc., v0.5.1-docker)
  scan: Docker Scan (Docker Inc.)

Server:
 Containers: 3
  Running: 3
  Paused: 0
  Stopped: 0
 Images: 76
 Server Version: 19.03.13
 Storage Driver: overlay2
  Backing Filesystem: xfs
  Supports d_type: true
  Native Overlay Diff: true
 Logging Driver: json-file
 Cgroup Driver: cgroupfs
 Plugins:
  Volume: local
  Network: bridge host ipvlan macvlan null overlay
  Log: awslogs fluentd gcplogs gelf journald json-file local logentries splunk syslog
 Swarm: inactive
 Runtimes: runc
 Default Runtime: runc
 Init Binary: docker-init
 containerd version: 8fba4e9a7d01810a393d5d25a3621dc101981175
 runc version: dc9208a3303feef5b3839f4323d9beb36df0a9dd
 init version: fec3683
 Security Options:
  seccomp
   Profile: default
 Kernel Version: 5.8.10-1.el7.elrepo.x86_64
 Operating System: CentOS Linux 7 (Core)
 OSType: linux
 Architecture: x86_64
 CPUs: 8
 Total Memory: 31.1GiB
 Name: ip-10-113-199-224.evoforge.org
 ID: SIB6:JXQ7:PHVH:T3XS:3J4Q:3SPS:XFVX:QHDK:Z3EN:TP7R:W5ZG:NBRQ
 Docker Root Dir: /var/lib/docker
 Debug Mode: false
 Registry: https://index.docker.io/v1/
 Labels:
 Experimental: false
 Live Restore Enabled: false

WARNING: bridge-nf-call-iptables is disabled
WARNING: bridge-nf-call-ip6tables is disabled

Additional environment details (AWS, VirtualBox, physical, etc.):
AWS

Start by comparing the docker save and docker run entry points and reproduce the behavior with an image absent locally. Determine how image retrieval is handled before saving; done means docker save downloads a missing image and writes the requested output, with coverage for the reported command sequence.