Aligning multiple figures

The idea is to align the origins of all the tikzpictures by using a common cell size. First we determine the distances to the bounding box for each picture, then we add extra points to produce a common bounding box for each picture.

The resulting cell size is far too large for the page. Some savings can be obtained by doing each column separately, but it still won't fit inside the margins.

documentclass[letterpaper,11pt,english]{article}
usepackage[ascii]{inputenc}
usepackage[T1]{fontenc}

usepackage{subcaption}
usepackage{graphicx}

usepackage{pgfplots}
pgfplotsset{compat=1.15, small}

%usepackage{showframe}% MWE only

newcommand{xleft}{0pt}% reserve global names
newcommand{xright}{0pt}
newcommand{ybottom}{0pt}
newcommand{ytop}{0pt}

newcommand{maxborders}[1]{% #1 = csname to store left offset
  path (current bounding box.south west);
  pgfgetlastxy{x}{y}
  globalexpandafterletcsname #1endcsname=x
  ifdim xleft>xrelax globalletxleft=x fi
  ifdim ybottom>yrelax globalletybottom=y fi
  path (current bounding box.north east);
  pgfgetlastxy{x}{y}
  ifdim xright<xrelax globalletxright=x fi
  ifdim ytop<yrelax globalletytop=y fi}

begin{document}

example ref to fig ref{fig1}

begin{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  sbox0{begin{tikzpicture}[baseline]
        begin{axis}[ylabel={yname}]
          addplot {x};
        end{axis}
      maxborders{left0}
    end{tikzpicture}}
  sbox1{begin{tikzpicture}[baseline]
      pgfplotsset{set layers, scale only axis, xmin=-5,xmax=5,width=5cm}   % pgfplots' manual recommends those options: The Reference -> Axis Descriptions -> Two Ordinates
      begin{axis}[
          ylabel={$f(x)=x^2$},
          yticklabel pos=upper,
          ylabel style={font=Huge},
        ]
        addplot {x^2};
        label{x2}
      end{axis}
      begin{axis}[
          ylabel={$f(x)=x^5$},
          yticklabel pos=upper,
          ylabel style={font=Huge},
          axis y line* = left,
          ymode=log
        ]

        % add potential to legend. only legend entries of last axis will be displayed.
        addlegendimage{/pgfplots/refstyle=plot_x2}addlegendentry{$x^2$}

        addplot [red] {x^5};
        addlegendentry{$x^5$}
      end{axis}
      maxborders{left1}
    end{tikzpicture}}
  sbox2{begin{tikzpicture}[baseline]
      begin{axis}[xlabel=$x$,xlabel style={font=Huge}]
        addplot {x^3};
      end{axis}
      maxborders{left2}
    end{tikzpicture}}
  sbox3{begin{tikzpicture}[baseline]
      begin{axis}[yticklabel pos=upper]
        addplot {x^4};
      end{axis}
      maxborders{left3}
    end{tikzpicture}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  begin{tabular}{ll}
    begin{tikzpicture}[baseline]
      node[anchor=base west, inner sep=0pt] at ({csname left0endcsname},0) {usebox0};
      path (xleft,ybottom) (xright,ytop);
      draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
    end{tikzpicture}
  &
    begin{tikzpicture}[baseline]
      node[anchor=base west, inner sep=0pt] at ({csname left1endcsname},0) {usebox1};
      path (xleft,ybottom) (xright,ytop);
      draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
    end{tikzpicture}
  
    parbox{dimexpr xright-xleft}{% put captions is separate row
      captionof{figure}{textbf{Confusion Matrix foobar}}
      label{fig1}}
  &
  
    begin{tikzpicture}[baseline]
      node[anchor=base west, inner sep=0pt] at ({csname left2endcsname},0) {usebox2};
      path (xleft,ybottom) (xright,ytop);
      draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
    end{tikzpicture}
  &
    begin{tikzpicture}[baseline]
      node[anchor=base west, inner sep=0pt] at ({csname left3endcsname},0) {usebox3};
      path (xleft,ybottom) (xright,ytop);
      draw[red] (current bounding box.south west) rectangle (current bounding box.north east);
    end{tikzpicture}
  
  end{tabular}
end{center}

end{document}