That's to be expected because this is the Emacs Lisp reference, not the Emacs manual. It explains how a developer can adjust the vertical scrolling in a fine-grained way.
Emacs 26.1 introduced pixel-scroll-mode which demonstrates this capability.
The closest existing tool to what I have asked for is follow-mode:
Emacs wiki: https://www.emacswiki.org/emacs/FollowMode
Source in Emacs mirror on Github: https://github.com/emacs-mirror/emacs/blob/master/lisp/follow.el
M-x follow-mode to trigger manually
(setq follow-auto t) to trigger automatically
C-c . 1 or M-x follow-delete-other-windows-...
If you add the built-in scroll-lock-mode to your code, you should get behavior like what you want.
Here's a slightly more-expansive update to your mode that fixes two other issues I found (the buffer-local version works normally and it doesn't change recenter-positions globally). Following your comments, I've also updated it not to rely directly on scroll-...
The O.P. has indicated in a comment underneath the question that he/she has tried (and likes) the recommended setting (also set forth in a comment) of (setq scroll-conservatively 101); and, that the O.P. prefers that the setting be global (as opposed to just buffer-local for a particular major-mode). Many examples scattered over the internet use a value in ...
This can be done using scrolling commands written in elisp.
;; Scrolling that re-centers, keeping the cursor vertically centered.
;; Also clamps window top when scrolling down,
;; so the text doesn't scroll off-screen.
(defun my-scroll-and-clamp--forward-line (n)
"Wrap `forward-line', supporting Emacs built-in goal column.
Argument N the number of lines, ...
The O.P. has indicated in a comment underneath the original question that a previous suggestion by this author resolved the issue, and this answer is a write-up of that solution.... There is no need to use any advice-.... Instead, the O.P. could use one of two potential conditions:
For just one exception, modify the function line-change as follows: