Eye of Ender always moves to the world origin when summoned

I also was able to tell that /summon minecraft:eye_of_ender ~ ~ ~ {NoAI:true} still makes them go to 0, 0. Not sure if this is intentional behavior. Was able to replicate in 1.16.2, 1.15.2, and 1.14.4.

One thing you can do to make them stay still is using invisible item frames. You can do /give @s item_frame{EntityTag:{Invisible:1b}} place down the item frame wherever you like (even on a barrier to make it "float") and place a eye of ender in the invisible item frame, it will now stay still.

I was able to replicate in 1.7.2 → 1.16.2 (Singleplayer, /summon was added in 1.7.2)
I was able to find a workaround for my motion issue, I made the eye of ender ride an armor stand.
(Tags are use to kill the armor stand when the eye of ender of ender destroy itself)

/summon armor_stand ~ ~1 ~ {Tags:[A],NoGravity:1b,Marker:1b,Invisible:1b,Passengers:[{id:eye_of_ender}]}

Can confirm in 20w48a.

Can confirm in 20w51a.

Can confirm in 21w03a.

Can confirm in 21w06a.

In 21w11a

Can confirm in 21w16a.

Can confirm in 1.17.

Can confirm in 1.17.1.

This ticket is actually a duplicate of MC-172738. This information is mentioned in this ticket and it also has an assigned "Mojang Priority".

This is not a complete duplicate of MC-172738 because the Motion field seems to be read, but its value is most likely overwritten when the entity is ticked.
But the rest of this report is probably duplicating MC-172738, so I will leave it as Duplicate.