"The only way warp can "work" is if you deliberately design maps that force the player to use warp in certain spots and take the warp staff out of the player's hands in other areas that would otherwise break the game.
But what about Fates?
That game did Pair Up right, didn't it? Not really. Even if the Fates version of Pair Up is more balanced and better designed than Awakening's, it's still way too powerful. Dual Guard still makes juggernauting relatively easy since the stat boosts that can come from that can still be huge. Slow characters can become fast, characters that deal low damage can kill things, and thanks to the shields becoming consistent, a character with Dual Guard has better survivability.
Recap: Even when it's better balanced, Pair Up makes juggernauting far too easy. It's a mechanic that's so powerful that it always dominates the game's design. There's no drawback to using it, and because the game designs itself with the use of this mechanic in mind, not using it can put the player at a disadvantage.
The Rescue Mechanic
And here we have the more balanced, but still broken, older sibling of Pair Up: Rescue. The rescue mechanic could be best defined as:
"Rescuing allows playable units to pick up allied units – using the Rescue command – who are smaller than them, in order to protect them from harm or to carry them around the battlefield."
(Source: https://fireemblemwiki.org/wiki/Rescue_%28command%29)
Why is the mechanic this high up the list? In the hands of the right player, the rescue mechanic can do a lot! It allows players to move longer distances in shorter periods of time. Remember the # 5 spot on this list? The spot about fliers and mounted units? This mechanic gives them an even bigger advantage over infantry units because this is valuable utility they can use, and take advantage of, that infantry units can't. Fliers can even rescue infantry units across terrain like water tiles and mountains, making fliers even better than before.
Scylla did a great job pointing out another reason why rescue is busted: "Rescue also allows you to be far more aggressive with your positioning because you can just pull a unit out of a bad spot;"
What makes the mechanic even more powerful is when players start implementing rescue chains, where multiple mounted and flying units take a rescued character and ferry them across the map. It's pretty common among faster playthroughs, and this ultimately results in the player being able to beat entire maps in quicker periods of time. It also results in the player being incentivized to use mostly mounted and flying units, which is bad for the purpose of balancing.
Quick Recap: Rescuing is busted because it allows the player to move from A to B in far faster periods of time, erases the negatives of bad positioning, and makes mounted and flying units even better by giving them additional, powerful utility.
Moral of the Story: Ferrying mechanics are super busted, and Fire Emblem as a franchise would do well to remove them from future titles.
It's easy to see the appeal of a mechanic like this: It makes restarting less painful and time-consuming. If you're like me, you probably use this mechanic for this purpose. However, like bonus experience in Path of Radiance, there is a way for a more experienced player to use this in a way that completely breaks the game.
So yeah. This game essentially lets you fish for critical hits, and makes it easy to accomplish. Another issue is that Maddening mode of Three Houses seemed explicitly designed with this mechanic in mind. This led to the game implementing same turn ambush spawns, which is bad design. The next point about time rewinding is that it makes games easier, since resetting is less punitive and that so far the games where it's implemented have been really generous with how many charges the player gets. The obvious solution would be to give the player fewer rewinds on higher difficulties, but so far that hasn't happened.
a) Players can rush forward without any consequences.
b) This mechanic works as a way to force the probability to do what the player wants it to do.
c) It can be used to justify bad map design.
This is a mechanic so powerful that it will inevitably shape how the game plays, which is why it deserves to be so high up on this list.