Being a member matters because we have a record of the member’s baptism (anybody can
say they were baptized, but we know that members have been baptized, because we have their baptismal records) and members have been trained in Sacramental Prep and/or RCIA to discern whether they need to go to Confession or not, and have at some point in their journey been given an Examination of Conscience to use that shows them how to know whether they can receive Holy Communion.
Non-members can say, “I have discerned that I can receive” but we don’t know what their basis for discerning is (it could be “I feel nice today; therefore I am in the state of grace”), and we already know that they don’t go to Confession.
But if a member says they have discerned that they can, we know that they went to Confession if they thought they needed to, and we know that they used a proper Examination of Conscience to discern whether they could receive or not - and if they didn’t, well, it’s not because they didn’t know how or why, and the responsibility belongs to them; they answer to God for that, and it’s not due to any lack of training from us.
That’s why being a member is important.
On that note, outside of a very few members of RCIA (persons discerning whether to become Catholic), I have never
yet heard of a non-Catholic who thought he should be allowed to go to Confession, even though he’s not Catholic, and not thinking about becoming Catholic.

:ehh:
Ultimately, the Church is responsible to Christ for the right handling of the Sacraments. That’s why it’s so important to the Church that all members be properly educated in the use of the Sacraments, and that non-members be assumed not to know what’s going on, and treated accordingly.
If someone wants to receive the Sacraments in the Catholic Church, it is perfectly possible for them to become Catholic. If it’s important enough to them (if they take the Sacraments as seriously as the Church does), then they will.