One point that I don't think has been addressed is that trees are much better for persistent data structures. That is, immutable structures. A standard hash table (i.e. one that uses a single array of linked lists) cannot be modified without modifying the whole table. One situation in which this is relevant is if two concurrent functions both have a copy of a hash table, and one of them changes the table (if the table is mutable, that change will be visible to the other one as well). Another situation would be something like the following:
def bar(table):
# some intern stuck this line of code in
table["hello"] = "world"
return table["the answer"]
def foo(x, y, table):
z = bar(table)
if "hello" in table:
raise Exception("failed catastrophically!")
return x + y + z
important_result = foo(1, 2, {
"the answer": 5,
"this table": "doesn't contain hello",
"so it should": "be ok"
})
# catastrophic failure occurs
With a mutable table, we can't guarantee that the table a function call receives will remain that table throughout its execution, because other function calls might modify it.
So, mutability is sometimes not a pleasant thing. Now, a way around this would be to keep the table immutable, and have updates return a new table without modifying the old one. But with a hash table this would often be a costly O(n) operation, since the entire underlying array would need to be copied. On the other hand, with a balanced tree, a new tree can be generated with only O(log n) nodes needing to be created (the rest of the tree being identical).
This means that an efficient tree can be very convenient when immutable maps are desired.