So other than the aircon unit, what other loads do you have to power?
Modern lighting is negligible if you have LED bulbs.
Hot water tank, clothes dryer, oven, range, and other appliances, if you pay a little bit of attention, can all be run one at a time on a 5kw gen no problem.
Not too many other heavy surge startup items in most homes other than an aircon, and with a soft start kit they can be run on a lot less generator than you might think.
About the only thing that might trip up a 10kw military diesel on a modern house is if the aircon is a heat pump type, and being operated in colder weather. Heat pumps don't work well in the cold, so they use heater strips, which can be multiple 50 amp 240V strips. Over 24kw draw just for the heat pump.
For comparison's sake, an MEP802A will handle 2 3 ton Nordicair ECU aircons, and the 803A can handle 4 of them all running at the same time. The compressor startup surge is so short that it pretty much never overlaps enough to cause any issues.
If you want something that you can just turn on and not worry about managing loads and whatnot, you might be better off with a civilian home standby generator with auto transfer switch. No wet stacking, the fuel never goes bad, and much easier to find someone to work on it when it needs service or repairs, plus much better parts availability.
(I'm a certified Generac tech, so I do have a little experience with generators on houses)