GW1 had way fewer attributes to spend points on, but if you did, you would increase the damage and crit chance of certain weapons or the power (damage, healing, duration, ...) of certain abilities. What I was mainly referring to (and what I would like in GW2, too) was the principle of freely spending a budget (with increasing cost) on attributes which improve certain offensive or defensive abilities. Anytime you want outside of combat.

GW1 also has/had Runes and Insignias which require(d) (perfect) salavage kits to move around and hence are/were less flexible. But this has/had less impact on your build than the distribution of attribute points.

Originally GW2's trait system also had stat increases baked in, but this was later removed and more attributes (precision, ferocity, concentration, expertise) have been added.

So why not replace Stat Sets, Runes and Sigils as they are now with freely distributable attribute points and let Relics and whatever the successor of Sigils will be have unique (not stat-related) effects?