I find it much simpler to deal with this style than with the equivalent in other languages, which would scatter the details across a half-dozen files, a dozen classes, and two dozen methods.
As far as spending more time reading Clojure than writing it I experience this myself - and I'm pretty sure this isn't a bad thing.
When I consider adopting a language, part of that consideration is how well I can read others' idiomatic code. It's so important for understanding libraries. I'm still just having a hard time with Clojure. I know it clicks for a lot of people though.
The problem with your let strategy is this can also impair readability if you use too many as the code becomes too far indented to the right (lets inside of lets inside of lets).
But I guess in these situations you can just use transients that are first defined to nil. Some people will probably yell at you for this.