I've pushed the patch that fixes this.  The commit message hints at the
steps needed to prevent a resurgence of this bug when more developments
in eldoc.el are performed:

Author: João Távora <joaotavora@gmail.com>
Date:   Sun Jul 19 00:48:43 2020 +0100

    Don't needlessly request docs from ElDoc functions

    Fixes: bug#42421

    Do this conservatively for now: if the ElDoc helper buffer (as
    returned by eldoc--doc-buffer) is visible and showing documentation
    for the very same "situation" (as computed by the the new
    eldoc--request-state helper), don't request that documentation from
    sources again.

    Before this change, not only was that request inefficient but if the
    user invoked scroll-other-window to see more of the helper buffer,
    that would eventually cause it to be reformatted and unexpectedly
    recentered.

    Later on, when a customizable list of documentation "sinks" is offered
    to the user, say, something like eldoc-display-functions, this process
    must be consolidated.  In those circumstances, as soon as one of those
    sinks signals that it doesn't have up-to-date documentation for the
    state computed by eldoc--request-state, documentation will have to be
    requested anew from eldoc-documentation-functions via
    eldoc--invoke-strategy.

    * lisp/emacs-lisp/eldoc.el (eldoc--request-docs-p): Rework from
    eglot-display-message-p.
    (eldoc--last-request-state): New variable.
    (eldoc--request-state): New helper.
    (eldoc--handle-docs): Memorize state of request in doc buffer.
    (eldoc-print-current-symbol-info): Pass a token to
    eldoc--request-docs-p.
    (Version): Bump to 1.6.0

On Sun, Jul 19, 2020 at 1:03 AM João Távora <joaotavora@gmail.com> wrote:

> Hello, I'm following up on a bug started in
> https://github.com/joaotavora/eglot/issues/445.
>
> In the latest ElDoc, when the *eldoc* buffer is showing a lenghty
> docstrings for some situation in a source buffer, switching to that
> buffer scrolling around, then switching back to the same position in the
> source buffer will lead to that very documentation being re-requested,
> ultimately undoing the scrolling work done previously by the user.
>
> The attached patch prevents needless, superfluous doc requests when the
> requester's state is found to be identical to the state recorded in a
> visible *eldoc* buffer.
>
> These kinds of situation must be taken into account when redesigning the
> mechanism for allowing multiple outlets for documentation.
>
> For now, the patch should fix the situation.  Felicián, please try it
> out.  Notice that it probably needs the Emacs master version of eldoc.el
> (where, BTW, I have already fixed the other bug you report in the Github
> issue).
>
> João
>
>

-- 
João Távora