Memorizing music doesn't have to be forced. If you know a tune well and how the LH accompaniment is put together, you can sit down and play it without thinking about the song or practice it for a week to get it into your head.
There are several Pop songs I've learned that are arranged in a simple way. Once I was invited to a gathering and played a Pop song by ear without the sheet. It's not my favorite song but nonetheless the arrangement is very simple with LH arpeggios throughout. Once you learned the sequence, the rest are just repetitions.
There was a video by the piano teacher Jazer Lee from Australia. He said that people who appear in a talent show like "America's Got Talent" or "Britain's Got Talent" wouldn't perform on stage with sheet music. Otherwise the performer would look unprofessional.
When I started learning violin in strings class, everybody around me had to learn to read and played from the sheet. I assumed this is the norm but soon discovered that I was a natural memorizer. Over the years I've seen many student performance videos. Some are really good readers. Their eyes are locked to the sheet while playing expressively. Others play well without the sheet. When I was young, I thought that reading off the sheet was the only way to play pieces. Over the years I've played pieces at gatherings and on public pianos without reading a note. Today I'd play mostly from memory although I carry a lot of music PDF files on my phone just in case.
Depending on the way a piece is arranged, some pieces are just easier to memorize. Anything with a lot of repeated notes, chords or intervals is easy to remember. A piece like Bach Prelude in C out of WTC Book 1 is an easy piece to memorize simply because of the repetition. A piece out of Bach 2-part Inventions such as #4 or #8 is challenging to remember dispite playing just 2 notes at a time (1 on each hand). A piece like the Bourrée out of Lute Suite #1 (BWV996) in "First Lessons in Bach" is relatively easy to memorize. The piece has 2 lines (1 for each hand) except for the ending chord..
