Clojurians Log v2

I'm confused about why something I'm doing fails with (take!) but works fine with (go (<! ...)). Here's what I'm doing:

(require '[clojure.core.async :refer [go put! take! chan]])

  ; f is a function that will call itself asyncronously. In real usage, the put!
  ; is happening else-where and we want to free up the thread f is running on while we 
  ; wait for that put.
  ; I know that this example can be represented as a loop rather than as a recursion,
  ; that's not the point.
  ; If you run this, it will never print "done." 
  (defn f [v]
    (if (< v 100)
      (let [c (chan)]
        (put! c (inc v))
        (take! c f false))
      (println "done")))
  (f 0)
  ; => nil
  
  ; If you re-write f as follows however, it works. I want to understand what the difference
  ; between the two is:
  
  (defn f' [v]
    (if (< v 100)
      (let [c (chan)]
        (put! c (inc v))
        (go (f' (<! c))))
      (println "done")))
  (f' 0)
  ; => clojure.core.async.impl....
  ; done