Using Docker with Snakemake (as motivated by the Snakemake documentation) does not provide a true docker container?

In order to improve the distribution of my snakemake workflow, I am wanting to Docker-ize it. The way I usually deploy my software stack is through conda environments (saved as .yaml files within an envs/ directory of my project folder). They are then called by each rule through the conda: directive and --use-conda flag (at execution), for example:

rule exampleRule:
    input: input.file
    output: output.file
    conda:
        os.path.join(workflow.basedir, "envs/<nameOfEnv>.yaml")
    shell:  "some shell command"

Following the snakemake documentation, I am aware that I can Dockerize my full workflow using the command: snakemake --containerize.

The resulting Dockerfile is something like this (this is a contrived example, in reality I have seven environments that are all built inside this container):

FROM condaforge/mambaforge:latest
LABEL io.github.snakemake.containerized="true"
LABEL io.github.snakemake.conda_env_hash="dc12f3c8b1fb3caed02ab3305e24859bd63f4f1ea0c1ed29d71c857e7d0baaf5"

# Step 1: Retrieve conda environments

# Conda environment:
#   source: envs/nameOfEnvironment.yaml
#   prefix: /conda-envs/4e57ed29df8b6f849000ab15b5c719f2
#   channels:
#    - conda-forge
#    - bioconda
#    - anaconda
#    - defaults
#   dependencies:
#     - wget
#     - packageX == 5.3.0
#     - packageY == 2.5.5
#     - packageZ >= 1.1.1

RUN mkdir -p /conda-envs/4e57ed29df8b6f849000ab15b5c719f2
COPY envs/nameOfEnvironment.yaml /conda-envs/4e57ed29df8b6f849000ab15b5c719f2/environment.yaml

# Step 2: Generate conda environments
RUN mamba env create --prefix /conda-envs/4e57ed29df8b6f849000ab15b5c719f2 --file /conda-envs/4e57ed29df8b6f849000ab15b5c719f2/environment.yaml && \
    mamba clean --all -y

I have already succeeded in following this method, and built an image that I host on Dockerhub that is then referenced in the Snakefile, e.g. container: "docker://myDockerHub/myWorkflow_dockerimage:latest"

Then, when executing with the --use-singularity flag, snakemake will pull this image and build the environments.

The problem is that the rest of the execution seems to follow a similar procedure as if I had not used singularity/docker whatsoever.

Meaning that in order to run the workflow in this way, I still require some base packages being installed, most especially Snakemake itself. Doesn't this sort of defeat the purpose of containerizing the workflow in the first place, or do I misunderstand something fundamental?

The only real solution I can think of is to create an image/container with Snakemake installed. Then I would run this image using singularity - but from then on I would be running the workflow from within the snakemake image as if I had not containerized the environments themselves. When executing snakemake from within this image, I cannot use the --use-singularity flag, as singularity itself is not available from within the image.

It seems completely counterintuitive to run snakemake without the --use-singularity flag, when my intention is to utilize singularity.