If you have an expectation as to how fast the tank should be pulling, then go pug one yourself.
If you think a tank can go faster, then talk to them.
Do not tell them to hurry up, but inform them that the group is capable of keeping up and ask if they are able to do that.
If a dps chooses to pull something that they are not intending to deal with themselves then generally it should not be the job of the tank to deal with that.
It is nothing to do with terrible tanks, but dps who need to learn their role.
This coming from someone who mains a warlock and tries to appreciate that I am just 1 part of a group.