Why is there no \dollars in LaTeX

The reason is good old ASCII code that has a slot for $, but no slot for £.

Since $ has a special meaning for TeX, Knuth decided that in order to obtain the “$” glyph one just needed to escape $, so to type \$.

The pound symbol is available in fonts, but there used to be no straightforward way to input it (remember that when TeX was born there was no Unicode and code pages extending ASCII differed wildly among operating systems). Hence the solution was to define a control sequence for it.

There is no need for \dollars: I don't think you believe that typing \dollars is more practical than typing \$.

Now that we have Unicode and UTF-8 it's much simpler to type £ instead of \pounds.

\documentclass{article}

\begin{document}

\$100 is good, but £100 is better.

\end{document}

The LaTeX kernel has \textdollar, as well as \textsterling, \texteuro, \textcent, \textyen and \textdollaroldstyle for a dollar sign with two bars.

On older kernels, you might need to include the fontspec or textcomp packages to use some of these.

FWIW, dollars and pounds are on equal footing in ConTeXt:

\starttext
\textdollar 100 is good, but \textsterling 100 is better.
\stoptext

or an Wolfgang Schuster mentions in the comments, use \asciimode and directly enter the symbols:

\asciimode
\starttext
$100 is good, but £100 is better.
\stoptext