Significant overhead implementing Catalan numbers with histomorphism

Question

I'm exploring recursion-schemes recently and want to find some use cases for histomorphism - for which I think Catalan numbers could be a fun one (I'm aware there are better ways to implement Catalan numbers, which are not the focus of this question). What I come up with is the following:

import Control.Comonad.Cofree
import Control.Monad
import Data.Foldable
import Data.Function.Memoize (memoFix)
import Data.Functor.Foldable
import GHC.Natural

type Nat = Natural

-- unrelated lines omitted

catalanHisto :: Nat -> Nat
catalanHisto = histo \case
  Nothing ->
    1
  Just fs ->
    let xs = toList fs -- this is line 101 in my original code.
        ys = reverse xs
     in sum $ zipWith (*) xs ys

catalanMemo :: Integer -> Integer
catalanMemo = memoFix \q n ->
  if n == 0
    then 1
    else
      let xs = fmap q [0 .. n -1]
          ys = reverse xs
       in sum $ zipWith (*) xs ys

main :: IO ()
main = do
  -- print $ catalanMemo 1000
  print $ catalanHisto 1000

Performance suffers however, with catalanHisto:

real    49.36s
user    416.48s
sys     99.38s

which is pretty bad comparing with catalanMemo:

real    0.84s
user    5.09s
sys     2.08s

Given that at least it terminates, the histo version definitely memoized something, but there is a huge overhead that I'm not sure whether I'm misusing histo, or it's just the price to pay for writing programs this way. As I went ahead with some basic profiling:

    Sat Feb 19 22:58 2022 Time and Allocation Profiling Report  (Final)

       demo +RTS -N -s -p -RTS

    total time  =       20.78 secs   (52462 ticks @ 1000 us, 24 processors)
    total alloc = 122,870,767,920 bytes  (excludes profiling overheads)

COST CENTRE       MODULE                 SRC                                     %time %alloc

catalanHisto.\    Catalan                src/Catalan.hs:(101,5)-(103,31)          68.0   71.5
foldMap.go        Control.Comonad.Cofree src/Control/Comonad/Cofree.hs:301:5-46   28.4   25.0
catalanHisto      Catalan                src/Catalan.hs:(97,1)-(103,31)            1.7    0.0
catalanHisto.\.ys Catalan                src/Catalan.hs:102:9-23                   1.3    3.3

Not an expert interpreting those results, I guess in addition to some allocations in Control.Comonad.Cofree, it spents a majority of time doing allocation in the non-trivial branch of catalanHisto, probably due to toList and reverse, which I'm not sure how much room there is for optimization.