It's so disappointing that there isn't an economical, drop-in or maybe "semi-portable," small, water-cooled, diesel generator. I think 2kW would be fine for many folk, 3kW would probably take over the market.
I confess that among the things I hate about boating is when someone cranks up their Honda generator on their sugar-scoop transom, or deck, or flybridge, in an otherwise tranquil anchorage. Now, when I look for a spot to anchor, I studiously avoid being near a boat with a Honda on it, or with gas cans on deck. I truly hate the obnoxious hum that breaks the tranquility. On the other hand, while I've noticed the "plop, plop" of inboard, water cooled generators going on nearby boats, it is not disruptive at all.
But thank goodness for Honda - their products are pretty quiet, and they seem to strive to achieve this characteristic. I've actually confronted a nearby boater who was running a cheap-o 3kW generator mounted on some homemade, Rube Goldberg mount higher than their transom, broadcasting an intolerable racket, like the hammers of hell, across the entire anchorage. Air horn beats generator. When it finally stopped, other boaters applauded and sounded their horns in celebration.
About charging batteries with them: unless you are running a 50A+ AC charger, I think you are fooling yourself. Cruising with a plan to charge batts using your typically 10 or 20A shore power charger would, I think, require you to run the generator eight hours a day, no? Hair dryers and vacuum cleaners, microwave ovens, coffee makers, toasters? A good inverter works just fine, although it probably exceed the cost of an EU2000i, and requires a good house bank, good, high current alternator and smart regulator, and attention to battery management.
Regarding danger, diesel exhaust contains about 1/28th the carbon monoxide of the exhaust of a gas engine. So while it's not harmless, it's generally much less dangerous than gas exhaust. This week I was appalled to see an anchored sailboat with a Honda generator running on the foredeck, with the forward cabin hatch wide open, yawning at the generator, swallowing all of the exhaust. A true Darwin-award candidate. God save the innocent victims of this fool!
So, there you have it. Some people don't like your generators. I totally get it in Florida, and other places, where A/C is almost a requirement. But then, maybe all the boats are buttoned-up and insulated from the noise.