If someone doesn't understand something of the following wall of text, don't hesitate to ask me in this thread or via pm. I tried to make it as easy to understand as I can.
tl;dr: you don't save time with port options after dying.
Well, instead of only talking, I did some tests in Tikal(Raksha Temple) and HoS (normal).
What did I do? I cleared the instance (thank you to the helpers in HoS) and then walked from the entrance to the last boss and took the time I needed for it.
I did this twice for both instances. One time with movement title (sigil master) and one time with movement title and dn ring buff.
The result I got:
Tikal without dn ring: 3:46 min
Tikal with dn ring: 2:43 min
HoS without dn ring: 6:20 min
HoS with dn ring: 4:44 min
If you can port to the last boss in Tikal, after clearing the rest of the instance, can you just start the next try of the boss?
No you can not.
Why?
Because you have to wait for the cooldowns of your skills. Since you died before it most probably means, that you need all your burst skills for the boss. So you have to wait 5 min before trying the boss again.
Did you save time with a port?
No you did not, because walking to the last boss still means that you have to wait for a while till you have all your skills rdy.
If you have to wait anyways, why not just port and then wait, instead of walking and then waiting a bit?
In my experience players tend to get bored more often, if they have nothing to do and are just waiting, resulting in them doing other stuff "fast" in between and coming back late. So in the end you loose time because you were waiting too long without doing anything (like walking to the boss).
Now you may say, HoS got ports, why not in Tikal?
Well, you have to look at the time, the instances were made. Back when HoS was new (easy and normal mode, not custom hard mode) the players did not have dn ring and I think they did not even have movement speed title. They did not even have kodex book to get back to the instance and they had to get to HoS from a spawn point somewhere in savage lands. So the port crystals really were helping the players to save some time.
When Tikal was released, everyone could easily have at least one movement title and dn rings were also already common.