When I was learning English (non-native speaker here), I was taught that there is concept called "parallelism" in English grammar, which in my own understanding means that if I want to combine two or more ideas into a sentence, the ideas need to have similar forms and structures.
Therefore, the following sentences conform to the parallelism:
He loves baseball like his father does.
He can play baseball like his father can.
He plays baseball as good as his father does.
However, as I grow up, I keep encountering spoken and written sentences that omit the final verbs:
He loves baseball like his father.
He can play baseball like his father.
He plays baseball as good as his father.
Now, the latter forms sound as naturally fine to me, to the point that the first of the following sentences sounds better to me than the second one:
He is a good baseball player like his father.
He is a good baseball player like his father is/was.
Is it alright to omit the final verbs from the "X like Y" and "X as [adjective] as Y" sentences?