If your pump fails, chances are you can wait a few minutes (or at worst hours) and another cyclist with a pump will come along. The same doesn’t apply to tyres as this thread shows.
You can also reduce the chance of a pump failure to almost nothing by getting a good one (i.e. not an ultra-light mini-pump), cleaning and lubricating it, and checking it regularly for perishing rubber seals. That 99% of cyclists aren’t interested enough to bother doesn’t prevent you from doing this.
Handlebar failures can also largely be avoided by getting good ones in the first place (e.g. Nitto with a sleeve) and checking them for cracks periodically.
Tyres, on the other hand, are prone to misadventure at any time. This is especially true for lightweight tyres, which have enormous performance benefits unlike lightweight pumps or handlebars. So if you’re going to ride through the night far from home, I think carrying a tyre makes more sense than carrying many other items that others often carry, such as a second rear lamp (a reflector is enough insurance for me if my rear lamp fails).