Cannot modify the root tag of command storage

I thought it would be possible to modify and reference the root tag of command storage using the {} NBT path. As an example, set up the following data:

data modify storage test:test example_data set value 1b

Note that this can be displayed by using the {} path in a data get command:

data get storage test:test {}

However, this tag cannot be modified with data modify or data remove; all the following commands fail:

data modify storage test:test {} set value {other_data:2b}
data modify storage test:test {} set value {}
data remove storage test:test {}

The error message received from these is:

Nothing changed. The specified properties already have these values

I suppose that the inability to change the root tag to any value may well be intended, but it still should allow for the setting of a valid compound and allow the removal of the tag. Additionally, the error is uninformative (though that may constitute a separate issue).