The access level for a piece of metadata is locked to the access level for the associated entity by default (even if you try changing it to something else).

You can change that behaviour using the register_metadata_as_independent() function as is used in mod/profile/start.php, for example.

Personally I find independent metadata access levels confusing and would rather associate public metadata with a public entity but the feature can be useful sometimes.

Iff you are in need of a counter function only, you can also think about annotations as an alternative.

One of the simplest solutions for counters would be to use:

$counter = get_plugin_setting('counter','my_plugin');

//make calculations for counter if required

set_plugin_setting('counter',$counter,'my_plugin');