Does your level serve any purpose outside of PvE?

In Guild Wars 2 you can play PvE, WvW, and PvP. When you play WvW and PvP you are at level 80, not your actual level. So is your level meaningless outside of PvE, or is there some reason for me to level my character even if I only intend to play in PvP and WvW?

If you're just going to play PvP then your level doesn't matter, because you're boosted to level 80, and have all your skills and trait points unlocked. However, in WvW only your stats are boosted to level 80. You'll still need to unlock skills and trait points by leveling up, they won't automatically be unlocked when you're in WvW like they are in PvP.

Some elements of Guild Wars scale you up to max level to let you enjoy them fully without having to spend the time to get to the maximum level. Others don't. For most PvE stuff, you'll have to level normally: You can neither do dungeons nor progress in your personal story without leveling, and crafting would only be possible by either dodging mobs in high-level zones as you gather the materials, buying them from other players or receiving them from guildmates.

Regarding the PvP aspect, arenas require no level: they place everyone at an even playing field, as a level 80 character with appropriate gear. This mimics the PvP-only character mechanic that was present in GW1, where you could make a max-level, max-gear character that could only partake in PvP. For WvW, your stats get boosted to those of a level 80 character, but your traits and potentially skills lag behind: Still, leveling in PvE is not needed, as WvW, unlike arena PvP, gives you experience points (arguably a lot more than normal PvE).