Most Lisp-y language have multiple parsers. The frontend may be that one, or it might be another. Racket has hundreds of frontends [2], Scheme has Wisp [0], and so on.
The ideal part of it comes down to the language being able to manipulate itself. Make the tokens an array, that you can shift, inject and/or mould into what you need.
That being said, that power isn't isolated to just Lisp-y. A few stack languages have it, like Forth, or to plug myself [1]. However, stack languages are a bit harder to optimise.
It isn't that they don't want a complicated parser. It's that you want to be able to easily modify that parser as its running, without hitting TeX levels of performance slowdowns.
[0] https://srfi.schemers.org/srfi-119/srfi-119.html