TikZ: How to reverse arrow direction without switching start/end point?

To have arrow's head on opposition side of the spiral curve, you only need to change -Latex to Latex-. However result is quite unexpected (read unusable) ...

It might be more acceptable solution to move the arrow head close to the end of the spiral. For this you can exploit the package decorations.markings:

\documentclass[tikz, margin=3mm]{standalone}
\usetikzlibrary{arrows.meta, bending, decorations.markings}

\begin{document}
    \begin{tikzpicture}[
decoration = {markings,mark=at position .84 with
             {\arrowreversed[black]{Latex[length=1.5mm]}}}
                        ]
\draw[postaction={decorate}]
    plot[domain=0:25,variable=\t,smooth,samples=101,
           {Latex[length=1mm]}-]
        ({\t r}: {0.002*\t*\t});
\end{tikzpicture}
\end{document}

First of all, I would like to argue that bent arrows look better, also in the original plot. But since the curve becomes singular at 0, this does not immediately work because of dimension too large errors. However, it does once we approximate the inner-most stretch by an arc.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,bending}

\begin{document}
\begin{tikzpicture}[scale=2]
    \pgfmathsetmacro{\myt}{pi}   
    \draw[{Latex[bend,length=2pt]}-] 
    (0: {0.002*\myt*\myt})
    arc({0}:{180}:{0.002*\myt*\myt});
    \draw  plot[domain=pi:25.1327,variable=\t,samples=75,smooth]
         ({\t r}: {0.002*\t*\t});
\end{tikzpicture}
\end{document}

And here is the original pic with a bent arrow.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta,bending}

\begin{document}
\begin{tikzpicture}
    \draw [domain=0:25.1327,variable=\t,smooth,samples=75, -{Latex[bend]}]
        plot ({\t r}: {0.002*\t*\t});
\end{tikzpicture}
\end{document}

Note that one should always load bending when one attaches arrows to curved paths, regardless of whether or not one bends the arrows, since otherwise the paths get distorted. Bending cures the distortion even when not explicitly used.