From the 1968 Hunter Davies official biography of the The Beatles:

Once it was made clear to Arthur Howes and to various other people that touring was over, the Beatles let it be known publicly. One of the reasons given was that their music had developed so much, using full orchestras and electronic devices, that they couldn't possibly perform it on stage any more.

This is true but the most important reason was that for a long, long time they had hated what they were doing. They disliked dragging round the world, appearing publicly in a glass box like a peep show. They disliked performing on stage in the same old way. They thought it was a farce, a mockery.

Additionally, The Beatles also felt that it didn't matter what they played anyway - they thought that the fans couldn't really hear the music anyway, because the PA systems of the time were primitive, and the screaming was so loud.

Said Ringo Starr in the 1995 Anthology TV documentary about why they stopped touring:

Nobody was listening at the shows. That was OK at the beginning, but we were playing really bad.

As a result, they barely bothered to learn new songs for their live sets (as can be heard on the live recording of their last concert from Candlestick Park), where only four of the eleven songs were from 1965-1966.

It's also fair to say that previous American tours also had a fair few covers, and that the covers played in the 1966 tour were an extension of those. In general, earlier setlists of similar length had significantly more covers. At The Hollywood Bowl, in August 1965, they played twelve tracks, of which three were covers ('Twist And Shout', 'Dizzy Miss Lizzy', and 'Everybody's Tryin' To Be My Baby'). At the Hollywood Bowl in August 1964, there were four covers ('Twist And Shout', 'Roll Over Beethoven', 'Boys' and 'Long Tall Sally'). More often than not, they had habitually started and ended sets with covers, and the reason there were only two covers in 1966 was that George Harrison now had a song he'd written himself to sing, 'If I Needed Someone' where previously he had sung a cover ('Everybody's Tryin' To Be My Baby', and 'Roll Over Beethoven'), while they had perhaps decided that Ringo drumming and singing at the same time - usually on 'Boys' - wasn't worthwhile. Or maybe Ringo couldn't be arsed any more.

So in the end I think it's a case of inertia - The Beatles did not care to make the 1966 tour a reflection of the Beatles in 1966, broadly speaking.