It is very common to play chords with one or more notes "missing". Just because a chord has 4 or more notes does not mean they all must be played every time the chord is played.

Sometimes note(s) are dropped because it is music for beginners, so it makes it easier.

Other times it is because the dropped notes would muddy up the sound, (especially true in the lower registers), other times simply for convenience in playing, and sometimes the sound calls for a sparser chord.

Ok, let's suppose you decide to pencil in that missing chord note anyway, and you play it and you think that it actually sounds nicer. Is this just a subjective thing then?

Or is it possible that the transcriber watching this would say "What the %#$% are you doing? That's just wrong!" And I'm referring to transcriptions, not compositions.

Maybe you could provide some specific examples? What's the note being left out ?

When there is a Chord notation above the music as your example provides, that does not mean that the chord is played with every note possible, at least not at that moment.

It simply means that some version or inversion or construction that includes some of those notes from the chord is being played starting at that moment.

In your example above, the Am7 chord is there, beginning with a minimum skeleton of the Am chord (A and C). The music then adds the E immediately following the first beat; Next on the second beat with the RH comes the G for the seventh tone, thus "fulfilling the prophesy" of Am7 as announced at the beginning of the measure.

So all the notes of the Am7 chord are present by the second beat...none are "left out" as you claim.

This creates a nice subtle progression. If you crashed in with the entire chord at the first beat, that subteley would be lost.

You have to look past the way of thinking that says every note of a chord must be there at the very first announcement of the chord. It often is not like that.

The chord reference simply says that such-and-such a chord is going to be developed starting now, and continuing until the next chord begins to be played, again either in completion, or in pieces.

In the second measure, there is no F note being developed at all for the Bb major chord. But anyways, I do get the essence of what you are saying.

In your example, the tabs above the score are for guitar. The tab for A7 shows that the E, & G are played by the guitar.

If you are playing piano without guitar or vocal, then feel free to play whatever you like.

When playing solo piano, the LH is best occupied in playing a strong, musical bass line. If you're in an ensemble with a real bass player it may play chords, but they will rarely be full close-position triads and 7th chords - they just tend to sound muddy in the lower register. Think more of using the LH to propel the rhythm of the music. The only time you would just plonk down a full chord in the LH is when playing an automatic keyboard which uses it to recognize the harmony you require.