Why some die intentionally at speedruns? What does it give?

As far as I can tell, dying while enemies are on the Map speeds them up, so they come out faster - I didnt test a whole lot, but will do soon.

Death give enemies short speed boost. It is called Rift Rush.

yes but I believe they have to be spawned in for them to gain the buff, if they spawn in while you are dead they dont get the buff

Yep, with Rift Rush, enemies not only get speed boost, they also ignore guardians/players