I've had my fair share of PC deaths, but I found that I cared more when I saw the same PC through a campaign from inception to ending. It mattered more to me. I often found that replacement PCs that came in later in a campaign had weak ties to everything; they weren't there when the bad guy betrayed the party, or when they all escaped the King's dungeon and were wanted by the law. They kinda just showed up and said "Oh, Evil Wizard Guy is evil? I guess we should stop them." and that was the attachment they had to the campaign.
That said, I don't necessarily think "this one time at band camp" is a wrong way to play, but for me it's unsatisfying. If all my character is was just a collection of anecdotes, it feels thin. I want him to be a hero or a protagonist, to matter to the story and not be instantly replaceable with Elf#762.