As you can see, you can use damage commands to make mobs chase you from a distance. But if I set the universalAnger rule to true, it doesn't work.

1. Apply this NBT to mobs:

   execute as @e[type=!player] run data merge entity @s {PersistenceRequired:1b,Attributes:[{Name:generic.follow_range,Base:200}]}

2. Now go far and let this command work:

   execute as @e[type=skeleton] run damage @s 0 minecraft:arrow by @p

   → The skeleton chases the player.

3. Set the universalAnger rule to true and go through step 1 and step 2 again
   → The skeleton doesn't chase the player.