Learn English – a good way to remind someone to reply to your email

The Oxford English Dictionary definition 1c of the verb copy includes:

to provide (someone) with copies of correspondence, etc., on a particular subject for information. (Common in office use.)

The entry has this supporting citation from a novel published in 1983:

LaSalle pushed a file jacket across the table, and Harper flipped through the pages.‥ ‘You'll copy me on all this?’ said Harper.

So the answers to your question are that copy followed by a human direct object is established and recognised and that it has been around for almost 30 years, and possibly longer.

The passive use leaves open the possibility that someone else has taken action to subscribe you.

In the electronic age, where spam is not only an everyday hassle, but is becoming a legal issue as well, it can be annoying to the assumed subscriber, as well as factually wrong, to send you en email describing you have actively subscribed.

The actual subscription may have been effectuated by a third party, benevolently or not, or even an automated system (although these seem to be getting outlawed nowadays.

I think that especially for those remembering the days of paper media, the concept of being subscribed rather than subscribing may be remembered in the form of gift subscription. If I give someone a subscription to a paper or magazine, they certainly are subscribed, but as certainly, they never did subscribe themselves.

From the point of view of the company that offers the subscription services (let's call them ACME), it is irrelevant who performed the action of subscribing. When their system receives a request for Alice to be subscribes, all they know is that they need to inform Alice that such a request was received and handled.

Now ACME can send two messages:

(A) You subscribed.
(B) You are subscribed.

In case Alice filled out the subscription form, statement (A) is obviously accurate. Statement (B) is also accurate, because from the point of view of ACME, Alice is subscribed.

Yes, if we ask Alice about what happened, she is unlikely to say "I am subscribed by Alice". But Alice is not sending this message. ACME is.

In case Bob filled out the subscription form in Alice's name, statement (A) is inaccurate, but statement (B) is accurate. In this case, Alice would be able to state that she is subscribed. Although she may not know by whom.

TLDR: there are reasons to assume that a subscription does not always result from someone subscribing themselves. So using the passive and leaving out the agent makes for a statement that has less chance of being inaccurate.