Your dumb parser may be quick the first time, but when you have to render a template 100 or 1,000 or 1,000,000 times the cracks will start to show. One main benefit of parsing and compiling templates is that you can cache the result of that stage on the server.
If you want to be really smart about it, the client shouldn’t even be downloading a .mustache template — it should download a .js file containing a pre-generated function which can be called with the context, returning the rendered template. Parsing the template on the client side makes about as much sense as parsing JSON or XML with a hand-written pure-JavaScript parser.