Do you think tank DPS is important in FFXIV?

Of course it is. Anything that pushes a boss' HP bar closer to zero is important. Concern yourself more with the question of what should you be willing to sacrifice for higher tank DPS.
Higher tank DPS at the cost of mitigation is a balancing act that varies from team to team and goal to goal. My personal tanking philosophy is to never do something that stresses my healers unless I have made them aware beforehand. Ask yourself what the costs and benefits of higher tank DPS in a given situation are and then open up a line of communication with your team about it.