Provide image with only rustup

Do you think it would be possible to provide Dockerfile that only installs rustup?

It would be useful for people who are fine with stable rustup but would like to use any version of rust via rust-toolchain file.

I'm not a Docker expert but I think it could be the same as the image in this repository except installing cargo. I've been using the example below for quite a while with cached several directories (--mount=type=cache,target="/usr/local/rustup" --mount=type=cache,target="/usr/local/cargo/git" --mount=type=cache,target="/usr/local/cargo/registry" --mount=type=cache,target="/src/target",sharing=private):

# syntax=docker/dockerfile:1.3

FROM buildpack-deps:bullseye AS builder

ARG RUSTUP_HOME=/usr/local/rustup
ARG CARGO_HOME=/usr/local/cargo

ENV RUSTUP_HOME=${RUSTUP_HOME} \
    CARGO_HOME=${CARGO_HOME} \
    PATH=${CARGO_HOME}/bin:$PATH \
    GIT_SSH_COMMAND="ssh -o UserKnownHostsFile=/dev/null -o StrictHostKeyChecking=no"

RUN set -eux; \
    dpkgArch="$(dpkg --print-architecture)"; \
    case "${dpkgArch##*-}" in \
        amd64) rustArch='x86_64-unknown-linux-gnu'; rustupSha256='3dc5ef50861ee18657f9db2eeb7392f9c2a6c95c90ab41e45ab4ca71476b4338' ;; \
        armhf) rustArch='armv7-unknown-linux-gnueabihf'; rustupSha256='67777ac3bc17277102f2ed73fd5f14c51f4ca5963adadf7f174adf4ebc38747b' ;; \
        arm64) rustArch='aarch64-unknown-linux-gnu'; rustupSha256='32a1532f7cef072a667bac53f1a5542c99666c4071af0c9549795bbdb2069ec1' ;; \
        i386) rustArch='i686-unknown-linux-gnu'; rustupSha256='e50d1deb99048bc5782a0200aa33e4eea70747d49dffdc9d06812fd22a372515' ;; \
        *) echo >&2 "unsupported architecture: ${dpkgArch}"; exit 1 ;; \
    esac; \
    url="https://static.rust-lang.org/rustup/archive/1.24.3/${rustArch}/rustup-init"; \
    wget "$url"; \
    echo "${rustupSha256} *rustup-init" | sha256sum -c -; \
    chmod +x rustup-init; \
    ./rustup-init -y --no-modify-path --profile minimal --default-toolchain none --default-host ${rustArch}; \
    rm rustup-init; \
    chmod -R a+w $RUSTUP_HOME $CARGO_HOME; \
    rustup --version;

Compare the existing Rust image Dockerfile in the repository with the Dockerfile example in this issue, including its rustup installation and architecture handling. Confirm how images are built and published, then verify that the resulting image provides rustup without a default toolchain and can honor a rust-toolchain file.