Forcing bmatrix to have a square form: Is there a canonical way in 2020?

Square matrices are often rendered as rectangular due to its asymmetric contents. I would like to automatically force these matrices to be square anyway using some canonical solution, i.e.,

1. the resulting matrix ought to look nice for most purposes;
2. is automatic (when an additional, optional argument is given for the squaring);
3. ideally, does not require me to define new environments myself (not compulsory);
4. has options for various xmatrix commands, e.g., x = b, B, p, or has similar syntax to xmatrix.

Here is a example picture of a non-desired outcome with bmatrix:

where the horisontal dimension clearly exceeds the vertical dimension.

There is an older question from 2014 whose answers do not meet some of the above criteria, either by defining new environments and probably not working for various types of xmatrix, or by being manual in essence. (The MWE in the accepted answer also does not compile).

I am willing to import any package if necessary. The solution should also work with Beamer.

• Question: Can the above criteria (1–4) be met in at the time of writing?

---

Here is an MWE to play around with which was also used to generate the example image.

documentclass{beamer}

begin{document}

    begin{frame}{Example}
        %Should look like square matrix but does not.
        $$
        begin{bmatrix}
            a_{0, 0} & dots & a_{0, n - 1}  
            vdots & ddots & vdots  
            a_{n - 1, 0} & dots & a_{n - 1, n - 1}
        end{bmatrix}
        $$
    end{frame}
       
end{document}

documentclass{beamer}
usepackage{array}

makeatletter
defenv@matrix{hskip -arraycolsep
  let@ifnextcharnew@ifnextchar
  defarraystretch{3.2}%
  array{*c@MaxMatrixCols{wc{3.4em}}}}
makeatother

begin{document}

    begin{frame}{Example}
        %Should look like square matrix but does not.
        [
        sbox0{$begin{bmatrix}
            a_{0, 0} & dots & a_{0, n - 1}  
            vdots & ddots & vdots  
            a_{n - 1, 0} & dots & a_{n - 1, n - 1}
        end{bmatrix}$}
typeout{(thewd0,thedimexprht0+dp0)}
box0
        ]
    end{frame}
       
end{document}