What is the strategic value of the move Memento?

Solution 1:

In competitive Pokémon, the value of Memento is in providing virtually any Pokémon with a free turn of set up, especially fragile Pokémon who would otherwise be at risk of taking a strong hit.

After using Memento, the next Pokémon will be switched in at the start of a new turn, instead of switching into an opponent's move. With the opponent's offensive stats halved, the new Pokémon can feel free to use moves like Substitute, Dragon Dance, Swords Dance, Agility, Calm Mind, and so on, maybe even Baton Passing the buffs to a stronger Pokémon waiting to sweep the enemy team. Substitute is especially strong in this scenario, since it blocks non-offensive moves and is unlikely to break with the opponent's lowered stats.

Memento remains mostly gimmicky, but it can provide a bit of breathing room that can prove invaluable in giving you the edge over the opponent.