execute score comparison

1. Add scoreboard objective "s" (dummy)
2. Summon >2 armor_stands
3. Set players score to 1
4. Set score of one armor_stand to 1
5. Run this command: /execute as @e[type=armor_stand] run execute as @s if score @s s = @p s run say hi
-> it doesn't run "say hi"
6. Kill all armor_stand exept for the one with score = 1
7. Run execute command (above) again
-> it outputs "hi"

Question: shouldn't this execute command do the same as the one above? it doesn't work either.
/execute as @e[type=armor_stand] if score @s s = @p s run say hi