Inconsistent behavior regarding the footline with themes of same kind (with a Table of Contents Sidebar)

As shown by the following MCEs, the Goettingen and the PaloAlto themes, both of the "with a Table of Contents Sidebar" kind, behave differently regarding the footline:

• the 1st one is "okay": the colored background sidebar goes to the bottom of the page,
• the 2nd one is not "okay".

Is there any reason for this behavior, which is annoying with PaloAlto theme that doesn't let the user nicely add e.g. frame numbers in the footline.

\documentclass{beamer}
\usetheme{Goettingen}
\setbeamertemplate{footline}[frame number]
\begin{document}
\begin{frame}
  \frametitle{Goettingen theme}
\end{frame}
\end{document}

\documentclass{beamer}
\usetheme{PaloAlto}
\setbeamertemplate{footline}[frame number]
\begin{document}
\begin{frame}
  \frametitle{PaloAlto theme}
\end{frame}
\end{document}

Start by comparing the Goettingen and PaloAlto theme definitions and compile the two minimal examples in the issue. Check how each theme handles the footline and sidebar height. Done means PaloAlto provides consistent bottom coverage while allowing the frame-number footline to display correctly.