“Uniqueness” in most TCGs is a complete misnomer. Sometimes, it’s called “unique per player,” which seems rather silly. “Unique” means There Can Only Be One. It doesn’t mean Everybody Has Some, But Only One At A Time.
Magic’s old Legendary rule was perhaps the crappiest of the lot. I play a Chandra, and if you play the Chandra, both die. I understand the idea of paradoxes but that’s harsh. They’ve fixed that now (see link), and the game will be much better for it.
What they don’t talk about is how this affects the story. That’s because gameplay is more important.
Star Wars CCG had uniqueness (even cards that you could have only two or three of), but it was divided into Light and Dark decks so that was seldom an issue. The story works best when there are two sides, and you can’t have the same guys I have anyway.* Just ask poor Lando Calrissian, one of my favorite characters that was rendered useless by Magic-style Legendary rules text.
Obviously, Netrunner benefits from the same kind of double card universe system. Runners and corps don’t hire the same people.*
The old Middle-earth CCG had a character declaration phase at the start which meant that if you and I had two identical Aragorn-based decks and you revealed yours first, my whole deck was prevented from working. That is one of the worst uniqueness rules.
On the Edge probably had a good story based system. Every character was named and truly unique.* If you’ve already played Cheryl D’Aubainne and I want to play one, I have to get rid of yours first. Does this screw up mirror matches? Well, it makes them more interesting. Besides, it takes another card to permanently kill somebody in OTE, so I like how the story works.
The TCG that managed uniqueness the best was Jyhad (later Vampire: The Eternal Struggle). Everything in that game was a struggle for dominance, so when you played a character that I already had in play, we’d both bid to see who controls her. A fun mechanic and totally in flavor and reinforcing the story. Of course, this is a gameplay pain in the butt and not suitable for most other games.
Star Trek CCG used the system that most games have used since, which is Everybody Gets One. Most of the time, this is just fine, because as the game gets more cards, the chance of a real mirror match is lessened. Besides, that IP has clones and time travel.
What usually happens is that you and I are playing in alternate, parallel universes (even if we’re not playing Star Trek). On my turn, it’s my Good Guys versus your Bad Guys, and the reverse happens on your turn. Our Frodos and Picards and Skywalkers never talk to each other anyway.
The final takeaway here is that TCGs are not good storytelling games. Even the ones based on IPs with great stories are about interesting conflicts with the characters you love from the original tales. TCGs are “what if” engines. When you make it difficult and unadvisable to play an important hero from a film or book, that’s a disservice to the game and the IP as well.
If you want stories, read a book. Watch a movie. Play a TCG to see what could have happened if things were different.
*There are always exceptions. These are TCGs we’re talking about here.