Slow retrieval of distinct on indexed fields

[Renars Jeromans]

Hello,

This is not an urgent problem, but it has always intrigued me...
It's simplified case, but it makes the point. Let us assume that we have a 
table

create table T (id unsigned int unique, name char(10));
create index i_name on T(name);

Let's insert into it say 5 mil rows with name field being just say 5 
distinct values AAA, BBB, CCC, DDD, EEE.

Now the question. Why a query like

select distinct name from T;

takes about 3 sec to return just a bunch of rows?
As I understand it, index contains all these 5 values, so just simple 
lookup into index should take fractions of a second.
Can anyone comment on this? MySQL team?

Thanks,
Ren