Plain and simple, sometimes things gotta die. Like in any game, offensive and defensive positions are constantly shifting. This is especially true in multiplayer games. Threats are cards capable of shifting a player into an aggressive position. Answers help to restore parity or initiate counter-offensives. Single-Target Removal attempts to answer opposing threats on a card-to-card basis, often for much less mana than the threat cost.
Mana is a limited commodity, and efficiency is important, but there are many ways to extract value out of spells. Sometimes, removal can be a source of card advantage, which can wind up being more important than mana advantage. When one card of yours does more than one thing, it can be worth that extra bit of mana.
Politics
Political removal provides a source of Intangible Card Advantage. For example, Chaos Warp answers a threat, but allows the opponent to flip a card off the top, which might just be another threat. When that happens, it’s like you did them a favor!
Universal
Sometimes, overcosted removal is useful because it helps the color answer a type of threat it has trouble answering. For example, Black typically struggles to remove Enchantments. A mono-Black deck like a Seizan card draw deck might sneak in an Introduction to Annihilation if they’re concerned about Smothering Tithe, which makes treasures when people draw!
Repeatable
Another reason one might run overcosted removal is that the piece of removal has an ability that allows it to repeat the effect and remove multiple threats. Replicate and Buyback are both abilities that use the effect over and over, but at a mana or alternative cost. Capsize is an example of a powerful bounce spell that can hit multiple targets and then end up in the hand from Buyback.
Advantageous
Overcosted removal can also be useful if it provides a form of card advantage. Sometimes, the 3-mana Repulse is better than the 1-mana Unsummon because it draws a card. If you care about cards in hand, are able to copy the spell, or can reduce the colorless cost, Repulse becomes more useful to the strategy than more efficient options.