My question is in the title. It seems the Trie tree is quite fit for string indexing, and why is it that no mainstream databases use it as an indexing strategy.
Disks or SSDs are read in blocks, and the B+Tree indexes that databases use are optimized according to that structure. The B+Tree minimizes the average number of blocks you have to read to perform a lookup. They also allow you to update the index without changing too many blocks, and maximize the utility of cache.
Tries don't have these advantages. The one advantage they do provide is compressed storage of common prefixes, but for the short strings that are usually used as DB keys, that isn't much of an advantage. Sometimes specialized index structures are built to compress common prefixes, but again they're designed around the block structure of the storage.