I never used to use screen protectors, have owned every iPhone since the original with no issues (I'm very careful to put the phone in pocket by itself, etc.) Then, I got an iPhone 8 and got several scratches in the first few days, and it bugged me to no end. It seems I'm not alone in experiencing this with iPhone 8 / X glass.
Therefore, I've decided to use a protector on XS Max. It's not perfect because, as you said, you can see the edges of the glass, especially around the notch.... but it's better than getting scratches.