Why are .gif files not supported?

Just to prove the opposite: Direct embedding GIF is possible, though not in PDF, yet in SVG output.

We just have to add a graphicx driver for embedding GIFs (static/animated) to be used with the dvisvgm backend.

For in-lining GIF data into the SVG output, the GIF file must be base64 encoded. Package media4svg provides a command for this that we make use of in the driver code. Also, the dimensions of the GIF must be told to graphics. Pkg graphics accepts <img file base name>.xbb files from which it reads the BoundingBox information. For a 480px * 360px image, the contents of the xbb file reads

%%BoundingBox: 0 0 480 360

---

Typeset example.tex listed below with

dvilualatex example
dvisvgm --zoom=-1 --bbox=papersize --font-format=woff2 example

or

latex --shell-escape example
dvisvgm --zoom=-1 --bbox=papersize --font-format=woff2 example

or even

xelatex --shell-escape --no-pdf example
dvisvgm --zoom=-1 --bbox=papersize --font-format=woff2 example.xdv

---

N.B. Firefox fails to play animated GIF embedded in SVG that is itself embedded in a web page (like TeX.SX). It looks like a bug. Use a Blink-based web browser instead, such as Chromium, Chrome, Opera or Edge. Or right-click on the image and open the SVG in a new browser tab.

---

Input file example.tex.

(Download GIF from https://upload.wikimedia.org/wikipedia/commons/d/d3/Newtons_cradle_animation_book_2.gif)

documentclass[dvisvgm]{article}

% download `Newtons_cradle_animation_book_2.gif' before typesetting:
%
% https://upload.wikimedia.org/wikipedia/commons/d/d3/Newtons_cradle_animation_book_2.gif

usepackage[a6paper]{geometry}
usepackage{graphicx}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% graphic[sx] driver for static/animated GIF inclusion
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
makeatletter
defGinclude@gif#1{%
  ifluatexelsebaseSixtyFour{#1}encodedGiffi%        
  dimen@Gin@urx pt%
  advancedimen@ by-Gin@llx pt%
  edefGin@svg@view@width{strip@ptdimen@}%
  dimen@Gin@ury pt%
  advancedimen@ by-Gin@lly pt%
  edefGin@svg@view@height{strip@ptdimen@}%
  dimen@Gin@svg@real@height@bp pt%
  advancedimen@ by-Gin@ury pt%
  edefGin@svg@view@base{strip@ptdimen@}%
  Gin@[email protected]@req@width%
  Gin@[email protected]@req@height%
  raisestrip@ptGin@req@height bphbox{%
    special{dvisvgm: raw
      <g transform="translate({?x},{?y})">
        <svg overflow="ifGin@clip hiddenelse visiblefi" width="strip@ptGin@req@width" height="strip@ptGin@req@height"
            viewBox="Gin@llxGPT@spaceGin@svg@view@baseGPT@spaceGin@svg@view@widthGPT@spaceGin@svg@view@height">
          <image width="Gin@svg@real@width@bp" height="Gin@svg@real@height@bp"
            xlink:href='data:image/gif;base64,{?nl}%
            ifluatexdirectlua{media4svg.base64("#1",72,"{?nl}")}%
            elseencodedGiffi'/>
        </svg>
      </g>}%
  }%
}
letGread@gifGread@bitmap
makeatother
RequirePackage{media4svg} % provides base64-encode utility
ExplSyntaxOn
letbaseSixtyFourmsvg_convert_file_to_blob:nN
ExplSyntaxOff
DeclareGraphicsRule{.gif}{gif}{.xbb}{}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% provide BoundingBox information in a separate file
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
begin{filecontents}[overwrite,noheader]{Newtons_cradle_animation_book_2.xbb}
%%BoundingBox: 0 0 480 360
end{filecontents}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

begin{document}

section{Animated GIF}
noindentincludegraphics[width=linewidth]{Newtons_cradle_animation_book_2.gif}

end{document}