I have looked at the problem that citations cannot be inserted as 1st items
in footnotes once again more closely. It has become obvious for me that
this is indeed a bug of org-cite or rather a default setting which was
deliberately introduced, although it is not really user-friendly or
practical to my mind.

I modified the function org-cite--allowed-p in oc.el  and inserted
'footnote-definition' in the following lines:

;; Paragraphs and blank lines at top of document are fine.
     ((memq type '(nil paragraph footnote-definition)))

(I leave the comment in its original form to make the passage easier to
identify.) 'footnote-definition' by the way does not appear anywhere in
org-cite--allowed-p in its current form.
After this I can easily insert footnotes as 1st items in citations, and I
do not get Org's warning "Cannot insert citation here".

Am Sa., 18. Sept. 2021 um 22:39 Uhr schrieb Bruce D'Arcus <bdarcus@gmail.com
>:

> Elias - do you mean org-cite-insert won't allow this?
>
> [fn:1] [cite:@doe2019].
>
> If yes, I don't see that; it inserts fine.
>
> I'm using bibtex-actions for the insert processor, but I don't think
> that should make any difference, since it's org-cite that's handling
> that.
>
> On Sat, Sep 18, 2021 at 4:23 PM Elias Bounatirou
> <elias.bounatirou@gmail.com> wrote:
> >
> > Hi,
> > When I try to insert a citation as the first item into a
> non-inline-definition footnote, org-ref-cite refuses to insert the citation
> returning in the minibuffer "Cannot insert citation here". The same problem
> does not occur if the footnote has an inline definition. As for
> non-inline-definition footnotes, if I copy the citation into the footnote,
> no problem occurs, either. The citation is also properly exported to LaTeX.
> > Is this a problem of org-cite/org-mode in general or rather of
> org-ref-cite?
> >
> > Best regards,
> > Elias
>