This does not relate to the command being executed at high frequency, the TP command is ran once and once only.
Reproduction:
Summon this entity block in a command block using this command:
/summon AreaEffectCloud ~ ~1.125 ~ {Radius:0.5f,Duration:2147483647,Effects:[],Particle:"take",Tags:["Block","BlockController"],Passengers:[{id:"Shulker",Invulnerable:1,NoAI:1,Tags:["Block"]},{id:"FallingSand",Block:"minecraft:stone",Time:1,Tags:["Block"]}]}
Now run this ONCE:
/tp @e[tag=BlockController] ~ ~1 ~
Nothing happens?
The teleport will only update after quitting and rejoining
Code analysis by @unknown can be found in this comment.
Linked issues
Comments

Thank you mrpingouin1
Has this been ignored? Nobody has assigned it yet
It's not being ignored. Assignment is no indication of this, only a very low percentage of fixed issues are assigned before fixing them.
It's not fixed?
Nobody claimed it was.

Confirmed for 16w06a
Please add some labels to this issue, as it's very hard to find
Please suggest some labels.
effect cloud teleportation rendering
Edit: fixed spelling of the word "cloud"
Important note: the AreaEffectCloud DOES get teleported! It's just the hitbox that doesn't get updated. If you testforblock, it will give you the correct answer and if you kill it with a radius, it will still be correct. So the position variables change and most other commands executing of that AreaEffectCloud will still work.

Confirmed for
1.10

Same reason as for MC-44654
confirmed for 1.11.2
Confirmed for 17w17b
Confirmed for 1.12 :C
Confirmed for 18w30b
Combining with MC-44654; it's the same issue.
Confirmed for 19w46b.
I also tried it with execute store Pos but it also turned out to be a failure.

@@unknown, this report has been resolved as duplicate of MC-44654. Please comment on that report in the future.
Confirmed, as you said, this is NOT related to MC-81075 because the commands don't have to be executed on the same tick. This bug seem to only affect AreaEffectCloud. Here is a cleaned command for better testing: