It does help you. You're following a dynamic programming solution. Suppose that the maximum dictionary word is of length k. Then for each position in the string you have a maximum of k previous positions that you're tracking for, "We could start a next word here."

Once you've scanned the string, only then do you discover whether the whole string is segmentable.

Put another way, while you're processing you don't immediately know whether or not the whole string is segmentable. But having a trie can let you discard possibilities early. Discarding work early means doing less work means being more efficient.