>> I could send a patch that fixes this bug.
>
> Thanks.  I hoped first to understand why we bind
> enable-recursive-minibuffers in these cases, but if you prefer to
> begin with a patch, please do, and let's take it from there.

To understand the problem, it's better to start from the manual.
The node (info "(elisp) Recursive Mini") says:

     If a command name has a property ‘enable-recursive-minibuffers’ that
  is non-‘nil’, then the command can use the minibuffer to read arguments
  even if it is invoked from the minibuffer.  A command can also achieve
  this by binding ‘enable-recursive-minibuffers’ to ‘t’ in the interactive
  declaration (*note Using Interactive::).  The minibuffer command
  ‘next-matching-history-element’ (normally ‘M-s’ in the minibuffer) does
  the latter.

And indeed the command ‘next-matching-history-element’ (‘M-s’)
mentioned as an example in the documentation, exhibits the same
problem reported by Richard:

0. emacs -Q
1. M-x                  ;; execute-extended-command
2. M-s                  ;; next-matching-history-element
3. C-x b                ;; switch-to-buffer

And it tries to read a buffer name, ignoring the default nil value
of ‘enable-recursive-minibuffers’.

This is because the manual documents the official way by binding
‘enable-recursive-minibuffers’ to ‘t’ that next-matching-history-element
does:

  (defun next-matching-history-element (regexp n)
    (interactive
     (let* ((enable-recursive-minibuffers t)
            (regexp (read-from-minibuffer "Next element matching (regexp): "
  ...

One possible solution is to support an additional value ‘transient’
for the variable ‘enable-recursive-minibuffers’.  Then this value
could have its effect only for the next invocation of
read-from-minibuffer.  Afterwards it will be set to ‘nil’
for any further recursive calls of read-from-minibuffer.

PS: Such transient value is similar to the value ‘lambda’ of
‘transient-mark-mode’ described in (info "(elisp) The Mark").

Currently this patch fixes the reported problem only
for the commands yes-or-no-p and next-matching-history-element: