Where it is clear that the past is intended, we don't always use the 'have become' form:
He denied doing it.
He denied having done it.
Here, it is clear in both that the action came before the denial, so we would often use the first form.
I would like to do it.
I would like to have done it.
Here, the same is not true, so we wouldn't have the choice. Where we have the choice, especially informally, we tend to use the simpler form.
