Are there situations where high-damage single attacks are better than multiple attacks that add up to more damage overall?

Concentration breaking.

The rules for concentrating on a spell state:

Whenever you take damage while you are concentrating on a spell, you must make a Constitution saving throw to maintain your concentration. The DC equals 10 or half the damage you take, whichever number is higher.

If a caster has a high Constitution modifier, it may be next to impossible to break their concentration without dealing very high damage. For example, the legendary archlich Acererak has +12 to Constitution saving throws, so he automatically succeeds on concentration saves from sources of damage that deal 27 or less damage at once.

On the other end of things, high damage can provide very reliable concentration-breaking against targets with low Constitution modifiers. I can recall numerous times during my time playing through Icewind Dale: Rime of the Frostmaiden that I wish I had a reliable method of breaking concentration on the frost druids we encountered. My DM just loved to hit us with a sleet storm spell.

This is probably the single most important mechanic that relies on dealing big damage in a single blow – at least, if hostile spellcasters are a regular feature of your game.

Punching a Balor (or similar creature)

There's a number of creatures that have automatic retaliation whenever they take a hit. For example, hitting a Balor in melee deals 3d6 fire damage. That'll add up if you make a lot of attacks per round.

Likewise, Armor of Agathys is the bane of low damage multi-attackers, with its automatic 5 points of Cold damage per spell level returned until you break it (which takes a set amount of damage)

Heavy Amor Master

The Heavy Armor Master feat gives the following benefit:

While you are wearing heavy armor, bludgeoning, piercing, and slashing damage that you take from nonmagical attacks is reduced by 3.

This is essentially the same as Damage Reduction from earlier editions. Since it reduces the damage from each attack by a flat amount, a single high-damage attack would be more effective against a character with this feat.

When you are attacking an object or vehicle

Many hard objects (DMG 247) and large vehicles (DMG 119) have damage thresholds, and don't take any damage from attacks that do less than this amount.

When you have a Chronurgy wizard and a 20 is needed to hit

Chronurgy wizards have a feature called Convergent Future which replaces a single attack roll with the minimum needed to hit. If the minimum needed to hit is a 20N, you can turn a single attack into a guaranteed crit (according to the most popular interpretation).

Suppose your total damage output with multiple attacks is greater than the damage output with a single, powerful attack but when that single, powerful attack becomes a crit, the total damage output for the single attack is more than the combined total for the multiple attacks, even when one of them has also become a crit. In this case it would be better to make the one attack and ensure it is a crit. For example, comparing great axe vs. two shortswords and ignoring damage bonuses, [d12] < [d6] + [d6], but [2d12] > [2d6] + [d6].

In a sense this subverts the question When is it better to do less total damage? by answering When it is actually more total damage. It is a specific example of the general case posited in the accepted answer by StephenTG, "If the character expects to...receive buffs that apply to a single attack...having that buff for "all" of their attacks for the round could be more valuable than just getting it for the first of many small attacks."

When the damage type or damage source matters

This isn't a function of the amount of damage per se, so not really a direct answer to the question, but there will often be a tradeoff, especially for casters, between spells that do a single amount of damage and spells that do smaller amounts of damage with multiple hits that total more. In general the total damage is the better option, until one considers the damage type or damage source.

For example, for a first level slot one could cast three magic missiles for a total average damage of 10.5, or one chromatic orb with an average damage of 9 (12.5 with a 75% chance to hit), but you have a choice of one of six damage types, to which the target might be vulnerable. For a second level slot, you could shoot three scorching rays with a total average damage of 14 - but if the target is immune to fire, a single acid arrow for less damage on average would be better.

When the rounding loss from damage resistance approaches the amount of damage that can be done

Suppose you are attacking a barbarian and have the choice of a single weapon that does 1d6 or two weapons that, dual-wielded, both do 1d3. Clearly 2d3 (individual average damage 2, total average damage 4) is more than 1d6 (average damage 3.5).

However, suppose the barbarian then enrages, such that all three weapons will be subject to their damage resistance. If the damage was just halved, the two attacks would still be better, but in 5e we always round down to integers unless otherwise directed, so a rolled 1 for damage will be treated as no damage after rounding down. In this case the average damage of the d6 becomes (0,1,1,2,2,3) = 1.5 while the average damage of 1d3 is (0,1,1) = 2/3. In this case the average damage of the 2d3 subjected to resistance is now less than that of the d6, and you would be better off using the single weapon for a single, large hit rather than the two weapons for two, smaller hits since they no longer total more.

This effect goes away for 'larger' dice since the chance of a rolled one becoming zero is less. Given the choice between a two-handed spear (1d8) and two daggers (2d4), the daggers are better before resistance but both options are equal after resistance (average damage 2). For larger weapons the two attacks would remain better even after resistance.

Instant Death

PHB p. 197:

Instant Death Massive damage can kill you instantly. When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.

Many DMs do not bother to roll death saves for monsters, and most monsters at higher CRs will have so much hp that the amount you can reasonably deal with a mighty blow will not suffice, but in games where the DM lets monsters stablilize and heal, killing them outright on a hit can be a benefit.

I think Thomas is right though, for practical purposes breaking concentration is the most valuable thing, and will matter most often.