Auto, if you did that, T2 strikers would have less than 5 HP without trinkets. As in, they get 2-hit by everything and 1-hit by heavy swords.
Regarding trinkets in lockdown
... Isn't the striker penalty supposed to reduce your health by 2/3 HP anyways?
Anything in tier 2 should at least boost your max health to 7. If the health is rounded up you would have 5HP without trinkets and unheated 2* gear at a rate of 33% decrease.
Only issue with striker is that it's designed to hit hard and fast but if you mess up or let someone get the upper hand, you are defenseless. When matched with health trinkets, your defense is your face instead of your feet. You can tank hits instead of dodge them, which isn't supposed to be a striker thing. A percent reduction, if done correctly, would likely balance strikers immensely.
I have faced some effective guardians and recons, and myself use recon more then striker. They balance it greatly by providing bonuses with bombs, swords, and health buffs and nerfs.
As a matter of fact, classes were mostly balanced before HP trinkets were created.
Although I've made a thread or two on this, I'll just sum up what should be done:
Each class should take their normal max HP level and then increase it by some percent. Strikers would receive a 33% DECREASE in max HP, while Guardians would get a 50% increase in max HP, and Recons would get a 0% to 33% increase, depending on what's balanced. This would mean that HP trinkets would be less effective on Strikers and more effective on Guardians and maybe Recons.