, I was
missing auto-complete a lot.
I managed to add this functionality by writing a simple function based
on compilation-read-command that uses completing-read instead of
read-shell-command.

Do you know about the `bash-completion' package?  It enhances
`read-shell-command' completion with completion data provided by bash.
It is very easy to set up,

   (use-package bash-completion :ensure t
     :init (bash-completion-setup))

should do it.

I was not aware of this, but it doesn't seem to do what I'm looking for.
For once, I am not using bash, but even ignoring that it doesn't seem
to have the effect I'm looking for.

I'm trying to get the compile prompt to suggest completion based on
past commands I've run.

My bad.  In that case, why not use C-r to search `compile-history'?

I'm not sure if you are suggesting that I should be able to use C-r in the compile prompt, if so there might be a keybind issue as I'm using evil and C-r does not do that for me.
If that's the case, could you name the function that does that? It could be what I'm looking for.

Then I used advice-add to overwrite the
original compilation-read-command with mine.

So far this works well, and as far as I can tell there is no good
reason not to make compile auto-completing, it already has a history
that you can navigate anyway.

With that said, this is the first time I write here and the first time
I'm trying to contribute to emacs, so I'm not sure what the best way
to go from here would be.
I think some decisions would need to be taken, for once I am not sure
if it's acceptable to change the default and make it completing or if
there should be an option for it.

I am not sure if you meant to attach any code, but that would probably
be the best place to start.

Looking forward to your feedback, thanks

You are right I should have posted code, so here is what I have:

  (defun compilation-read-command-with-autocomplete (command)
    "Use `completing-read` to add autocomplete powers to compilation read"
    (completing-read "Compile command: " compile-history
      nil nil command
      (if (equal (car compile-history) command)
        '(compile-history . 1)
        'compile-history)))

  (advice-add
    #'compilation-read-command
    :override #'compilation-read-command-with-autocomplete)

If this were added to Emacs, we probably wouldn't use advice.  I think
the best strategy for you would be to prepare a patch against compile.el
and add a user option that allows prompting the user with
completing-read.  What do you think?

I agree advice is not a good solution if this gets merged, this is just what I have in my config to make it work.

I believe an option defaulting to the current behavior is fine, assuming we don't want to just change it to the completing version all together.
However, I am somewhat lost on what that option might look like. Probably some customizable option based on which compilation-read-command's internals change to either the current or my version?

If so, I will need to figure out how the customizable system works internally in order to use it. Any pointers on that would be appreciated.