What you're saying directly contradicts what Essentials is saying
# If you do not wish to use a permission system, you can define a list of 'player perms' below.
# This list has no effect if you are using a supported permissions system.
# If you are using an unsupported permissions system, simply delete this section.
# Whitelist the commands and permissions you wish to give players by default (everything else is op only).
# These are the permissions without the "essentials." part.
# To enable this feature, please set use-bukkit-permissions to false.
Setting use-bukkit-permissions to false, according to this documentation, should disable all permissions plugins and grant the four named commands to all players without OP status.