Should `[arabic,main=english]{babel}` change the `plain` pagestyle?

Question

This is a follow-on from Table of contents page's number doesnt match the numbering style when i use foreign language "arabic". There the OP had difficulties with the page numbers of entries in the ToC. This a slimmed down version of the MWE which shows the problem and a solution.

% tocarabicprob2.tex  (based on SE 586620)
\documentclass[12pt,a4paper,twoside]{book}
\usepackage[Bjornstrup]{fncychap}
\pagestyle{plain}
\makeatletter
\let\origpsplain\ps@plain
\makeatother
\usepackage[arabic,main=english]{babel}
%%%%% try with and without this (arabic babel changes the definition of the plain pagestyle)
\makeatletter
\let\ps@plain\origpsplain
\makeatother
\usepackage{comment}
\begin{document}
\nocite{*}
\frontmatter
\addcontentsline{toc}{chapter}{Acknowledgment}
\centerline{\textsc{Acknowledgment}}
First
\clearpage
\addcontentsline{toc}{chapter}{Notation}
\centerline{\textsc{Notation:}}
Note
\clearpage
% this was in the original but did not affect any numbering
\begin{comment}
\begin{otherlanguage}{arabic}
\begin{center}
\Large{الملخص}
\end{center}
\begin{center}
\large{وبنيته وبعض البنيات الجزئية فيه.}
\end{center}
\end{otherlanguage}
\end{comment}
\tableofcontents \addcontentsline{toc}{chapter}{Table of Contents}
\mainmatter
\chapter{Preliminaries and Basic Concepts about Algebras}
blah
\end{document}

The OP's problem was that the page numbers changed from Roman to Arabic numbers with no intent on the part of the OP.

The basic problem here is that \usepackage[arabic,main=english]{babel} redefines the plain pagestyle (as noted by @Davislor in his answer to the original question). Why should the package interfere with the pagestyle and what could/should be done about it?