I guess this may well be a generational phenomenon, but I own a box of love letters. They cover my early boyfriends, back when boys and girls posted letters of feelings to each other! My first boyfriend at 14, my first 'love' at 15, and the rest of the significant (at the time) boys up until about 19. A whole box full. How retro.
I don't get love letters anymore (I do have a whole 'folder' of screen shot watsapp chats but not sure they carry the same sentiment!), but I suppose my current version are somewhat more permanent.
I can't imagine getting rid of my paper memories, nor can I imagine regretting my tattoo choices (linked to people no longer who I had hoped they would be). They remain markers in time, memories of happy moments unaffected by what came after them.
Photos of a partner with their ex, do not mean they were happier then, or wish they were still with them. Just that we all have our own journeys, and we share different parts of them with different people.
If you're newly shacked up, then of course I think polite ettiquette dictates that you keep these sort of mememtos hidden from view. That framed pic of you and your ex can no longer hang above your fireplace I'm afraid! But should you throw it away? Not if you don't want to.