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Lower exhaust temps doesn't necessarily equate to better efficiency. One reason is you're leaning out the fuel ratio. If you start out with 1 part fuel and 14.5 parts air you'll have hot exhaust because you're burning a lot of fuel in a volume that's only 14.5 times bigger than it. But then if you make it 14.5 parts air, 7.25 parts EGR and 7.25 para water, now it's 1 part fuel to 29 parts everything else. You get cooler exhaust because you're heating up a greater mass with the same amount of fuel. Kind of like turning on two range burners to the same setting and putting a bigger pot of water on one and a smaller pot of water on the other. After a minute has gone by the bigger pot will be cooler than the smaller pot because you were heating a bigger mass.
One problem with water is it's specific heat to expansion ratio is lower, about 1.3 instead of about 1.4 like air. So unless you change things like increase the compression ratio or advance the ignition timing you'll actually get worse fuel mileage.
Also there are efficiency losses the cooler you burn. Theoretically you want the flame as hot as possible for best efficiency. For an example, pure oxygen and pure fuel. But we don't have an affordable way of making an engine like that that's anything near practical. Too much cooling from water injection could hurt efficiency.
Still there are efficiency gains that can be made with water injection. One would be to replace high load enrichment with water injection. That way you could keep running a stoichiometric A/F ratio at wide open throttle. The increased CR and advanced timing possibilities are also important.
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