There are a handful of day flights to Europe ... American and British Airways have them out of New York and Boston to London. Although you feel a lot better when you arrive because you haven't lost a night of sleep, for most people, the cost of a European hotel room isn't worth the one night of mediocre/poor rest that comes with an overnight flight. Also, with exception to the eastern most cities in the US, it'd be difficult to leave in the morning and arrive in Europe at a reasonable hour that same night. Keep in mind too that the majority of the passengers on overseas flights are connecting onto them from other US cities that don't have direct international service ... because it'd be impossible to connect onto a morning departure to Europe, that means that the airlines are relying 100% on passengers that are originating in the departure city on the day of the flight. Demand just doesn't justify having more of these flights.
