My personal theory for the curved edges is, that samsung just wanted to prevent cheap off brand replacement screens.
Mine is that they wanted it to stand out, compared to all the other phones with flat screens at the time, especially with all the design clones.
You would look at it and go “oh that phone looks funny, must be a Samsung”.
This is what it was when they introduced it. I used to work for an Android OEM at the time and the product people really wanted to get their hands on curved screens for the same reason. Eventually they got Samsung to sell them some but it wasn’t as curved as the ones Samsung used on their devices to keep differentiation. It still cost twice what flat screens which ate a significant chunk of the profit margin.
The curved edges were the precursor tech to having a foldable screen. No matter what is said about the Apple vs. Samsung debate, Samsung is still the one responsible for the praises on Apple’s screens. They have tried with other manufacturers and providers but can’t escape the fact that Samsung is still the major leader on displays as they dump a shit ton of money on R&D on all LED screen technologies, specially manufacturing at scale. If you want high end screens, you just go with Samsung, period. The alternatives are constantly playing catch up with them and they are actually experimenting and trying to come up with new and original stuff. LG and Sharp are also really good, but their screens aren’t as premium as Apple wants them to be, though they are more affordable.