It's cool to be able to read, and it's cool to be able to play by ear. The more skills you have, the better. The important thing is that when you try to do something, to know why you are trying to do it. The idea behind not looking at the keyboard is to not use it as a crutch if you're trying to learn to read, so this becomes a huge rule of Forbidden Things (and there shouldn't be such a thing as Forbidden Things that we dread to do forever after no known reason). Reasons TO look at the keyboard is to be able to find distant keys, and reasons to look at your hands (esp. if you have the piece memorized when you are not trying to work on reading) is to look at how you are using your hands (and the rest of you).
If your aim is reading, then other skills tie into it. If you understand a bit of theory, and recognize a cadence or chord progressions, for example, then your music becomes predictable and your hands and ears will anticipate where they want to go. Don't be afraid to just explore the piano freely some of the time. Do you look for patterns in your music? For example, the piece you played has phrases that repeat. Can you hear them or see them? Seeing such patterns also helps you anticipate as you read, and make sense of the music.
Think of this:
Knock knock!
Who's there.
Banana.
Banana who?
Banana Banana.
If you are familiar with knock knock jokes, then you will predict "Who's there" and "Banana who." before the words are said. Music has a lot of predictable patterns like that and as you catch on, reading becomes a lot easier. I am staying out of the debate of whether you should learn to read. If this is your goal then some of these things might help.