Really? Looks to me like the lookup function is invoking recursion here: https://en.wikipedia.org/wiki/Trie#Algorithms

I would think the amortized cost would be O(log_b n), with b being something like the Shannon entropy of each symbol.

Well in that case the cost of a hash-function is also not O(1) since the minimum length of a n distinct keys is log(n).

Really both a trie and a hash-function boil down to O(m) where m is the length of the key.