I have seen lots of amateur pianists performing - both from memory and with score. The better ones tend to all play from memory - not really because they look impressive and flashy. It's some kind of energy or confidence coming through, and that makes the performance somehow different.
You've already hinted at it, but I'll be more forthright - when watching a solo pianist perform, most of us lower our 'expectations' down a notch when we see the performer read from the music, because we've been conditioned to expect soloists to perform from memory. And we then think less highly of their playing.
I never thought of that until a few years ago when I settled down to watch a BBC Proms concert broadcast live on TV. Richard Goode was playing Mozart's K488. With my back turned to the TV (I was making myself a sandwich - one should always have the equivalent of popcorn when watching a classical concert on the screen), I listened to most of the first movement, and thought it was nicely played. Sandwich prepared, I turned round to sit down..........and saw that Goode was laboriously reading from the score, with glasses on. I'd never seen a concert pianist perform Mozart from the score before, unless he was also the conductor.
Almost instantly, my impression of his playing went down. He seemed almost to be sight-reading, peering intently at the score. His playing sounded somewhat 'careful' and boring, and I wondered why I thought it was much better earlier, when I couldn't see him play. His tempo was slower than other pianists'.....or was it really?
A few days later, the BBC repeated that concert - on radio only, and I thought I'd listen again. With no visuals, I thought his playing was extremely fine - in the whole concerto.
No matter how 'immune' I thought I was, there was no getting away from the fact that I'm influenced by what I see.
Since then, I became a performer myself, playing a solo recital monthly - from memory. (Originally, because I didn't have my music with me, and in any case I don't have a page-turner). And I discovered that even those who knew no classical music were particularly impressed by the fact that I played from memory, showing that I was a 'proper performer' rather than a one-time student trying my hand at performing in public
. (My audiences in those recitals are mostly in a similar profession to mine, so they know I'm not a professional musician). And they listen more intently, and are more ready to be receptive to pieces that don't appeal immediately. And let's face it, classical music is rarely immediately appealing to those brought up on pop - there are no catchy riffs like pop/rock and even the nice tunes get 'mangled up' and submerged (as one of my younger listeners once told me).
So, despite the fact that it takes me on average five times as long to learn a piece to perform it from memory as it would to play from the score to the same standard, I never perform in public with the music in front of me - simply because my main purpose in playing the recitals is to introduce (and hopefully convert) audiences to classical music, and I want them to 'trust' my playing, and that I'm really 'into the music' that I play (for want of a better term). The few people in the audience who play the piano (or once played it when they were young) are even more receptive, because they knew how difficult it is to memorize even a short five-minute piece....and like those who aren't into classical music, the only classical musicians they knew of who performed from memory were all professional soloists.
In other words, for my purposes, I feel obliged to perform from memory, if I want people to listen to classical music seriously. (BTW, pop singers never perform from the music.....of course, they probably can't read music anyway
). That is unfortunately the legacy of Clara & Franz, and it's not going away anytime soon........