Proper way to build a CICD pipeline with Docker images and docker-compose

Question

I have a general question about DockerHub and GitHub. I am trying to build a pipeline on Jenkins using AWS instances and my end goal is to deploy the docker-compose.yml that my repo on GitHub has:

version: "3"

services:
  db:
    image: postgres
    environment:
      POSTGRES_USER: user
      POSTGRES_PASSWORD: password
    volumes:
      - ./tmp/db:/var/lib/postgresql/data
  web:
    build: .
    command: bash -c "rm -f tmp/pids/server.pid && bundle exec rails s -p 3000 -b '0.0.0.0'"
    volumes:
      - .:/myapp
    ports:
      - "3000:3000"
    depends_on:
      - db
    environment:
      POSTGRES_USER: user
      POSTGRES_PASSWORD: password
      POSTGRES_HOST: db

I've read that in CI/CD pipelines people build their images and push them to DockerHub but what is the point of it?

You would be just pushing an individual image. Even if you pull the image later in a different instance, in order to run the app with the different services you will need to run the container using docker-compose and you wouldn't have it unless you pull it from the github repo again or create it on the pipeline right?

Wouldn't be better and straightforward to just fetch the repo from Github and do docker-compose commands? Is there a "cleaner" or "proper" way of doing it? Thanks in advance!