Where a fixture is a long way from the water heater, a small dedicated unit under the sink solves a problem that no amount of central capacity addresses.
The problem it solves
The wait for hot water is the volume of pipe between the heater and the tap.
At a remote basin, a bar sink, a garage sink or a workshop, that can be a minute or more and several gallons down the drain each time — for a use that lasts twenty seconds.
The two forms
Mini-tank. A small storage heater, commonly 2.5 to 7 gallons, plugged into an ordinary receptacle. It stores enough for hand washing and a rinse, and it refills slowly.
Point-of-use tankless. A small electric instantaneous heater, sized for one fixture at a low flow. Needs a larger circuit than a mini-tank and stores nothing.
What they can and cannot do
They handle a basin. Hand washing, rinsing, a shave.
They do not handle a shower. The power required to heat shower flow instantaneously is far beyond an ordinary circuit, and a mini-tank holds only a few minutes.
They do not replace a central heater. They supplement it at one fixture.
Where they earn their place
A remote basin or bar sink, where the run is long.
A garage or workshop sink, which may have no hot supply at all.
An outbuilding.
A guest suite at the far end of a house.
As a booster ahead of a fixture needing hotter water than the rest of the house — a commercial-style dishwasher, for instance — where the main heater is set to a lower delivery temperature.
Installation
A mini-tank typically needs a standard receptacle under the sink, a cold feed and a connection to the tap's hot side. It also needs the relief valve arrangement its instructions specify, and it should sit where a leak would be noticed.
A point-of-use tankless needs a dedicated circuit sized from the nameplate, which for a basin unit is modest and for anything larger is not.
Both are simple installations, and both are permitted work in many jurisdictions because they involve a circuit.
Running cost
Small, because the use is small.
A mini-tank has a standby loss, which is real and modest on a few gallons. A tankless point-of-use unit has none, and needs a larger circuit.
Where the alternative is running several gallons of heated water down the drain each time the tap is used, either is an improvement.
The alternatives
Insulating the long run, which reduces the wait somewhat and does not eliminate it.
Recirculation, which addresses every fixture on the loop and costs more to install and to run.
Moving the water heater in a renovation, which is the right answer if a renovation is happening anyway.
A point-of-use unit is the cheap targeted answer for one fixture, and recirculation is the whole-house one. Choosing between them is a matter of how many fixtures have the problem.
Sizing a mini-tank
For hand washing at a basin, a 2.5-gallon unit is generally sufficient — it delivers a couple of minutes of warm water and refills while nobody is using it.
For a kitchen sink where dishes are occasionally washed by hand, a 4 to 7 gallon unit is a better match, since a sink of hot water is several gallons on its own.
The published recovery rate matters here as it does on a full-size tank: a small unit on an ordinary circuit refills slowly, and asking for two sinkfuls in a row will exhaust it.
Under-sink space
Both types occupy cupboard space that usually already holds a waste trap, a disposal and cleaning products.
Measure before ordering. A mini-tank is roughly the size of a small bucket and it needs clearance for its relief valve and its connections, and access for the occasional flush.