I am remodeling my kitchen. The location of the sink is about 25 feet from the hot water heater, and has always been a problem (more of an inconvenience) waiting for hot water to arrive at the sink. With the remodel, I am thinking of installing a small electric hot water heater directly below the sink.

I see a lot of Q&A about recirculating systems for secondary heaters, but I think what would work best for me is to simply run the main hot water feed into the inlet of the secondary heater, then outlet to the faucet. That way, I would have hot water quickly, although it would get diluted slightly with the cold water in the 25 foot of pipe, but then be replenished with hot water from the main heater.

Does this make sense?

Why not install a recirculation line from close to kitchen back to water heater.
Run 1/2 recirculation line from close to kitchen back to cold water input to water heater. Check valve in recirculation line and cold water input.

Install without pump. See if system works with gravity and siphoning action alone. If system does not work install small recirculation pump. Smallest you can get. Uses about same electricity as light bulb.

Why not install a recirculation line from close to kitchen back to water heater.
Run 1/2 recirculation line from close to kitchen back to cold water input to water heater. Check valve in recirculation line and cold water input.

Install without pump. See if system works with gravity and siphoning action. If system does not work install small recirculation pump. Smallest you can get. Uses about same electricity as light bulb.

I have considered this, but was looking at a small heater instead of a pump running 24/7.

Let me ask again. Do you think there would be any problem installing two heaters in series? Standard 50-gal gas heater supplying a small 2 or 3 gallon electric heater, hot out on the 50 to cold in on the 2-3?

Should be no problem with installing a small electric that way. Probably have to use a dedicated 20 amp circuit. Check amperage draw before purchasing.