The bonus for "upping" the HQ is actually a bit insignificant once you get past a certain point (around 30-40%, iirc). The extra-exp you earn whether you're at 100% or 40% HQ is so small that it barely makes up for the use of HQ materials (which can be significantly more expensive)

That is, if I recall things correctly, it's been a long time since I last had to level up my classes, SE may have changed some things a bit (that I'm not aware of)