CREATE TABLE t(

i int unsigned not null default 0

);

insert into t values(1),(2),(3),(5);

select i,UUID(),RAND() from t;

Output
1 6d0d7f6a-065b-11f0-b63b-a8a159823595 0.19175675994880195
2 6d0d7f94-065b-11f0-b63b-a8a159823595 0.5884875725847554
3 6d0d7fa0-065b-11f0-b63b-a8a159823595 0.3671676138110157
5 6d0d7faa-065b-11f0-b63b-a8a159823595 0.07037538203445765

As you can see, the UUID function is optimized out, other than RAND.
I guess UUID should work like RAND and generate an new UUID for each output line.