postgresql – Are reportedly “bloated” index sizes a problem?

I create a table with 1m records, then I delete those records. (Common with some sort of processing list.)

CREATE TABLE example (id int PRIMARY KEY);
INSERT INTO example SELECT generate_series(1, 1000 * 1000);
DELETE FROM example;
VACUUM example;

The index size remains at the same size as before deletion.

SELECT pg_size_pretty(pg_relation_size(c.oid)) AS size
FROM pg_class c
WHERE oid = 'example_pkey'::regclass;
 size  
-------
 21 MB
(1 row)

Likewise, bloat-detection queries (e.g. ioguix/pgsql-bloat-estimation) identify this index as extremely bloated.

I don’t care about the disk usage itself. Will the performance of the index be affected by its large size? Should I be running REINDEX?