Equinoxes and solstices: start of the season or mid-season? In the United States, the upcoming autumnal equinox is marked on most calendars as the "first day of autumn." Similarly the solstices are commonly called the "first day of summer" and "first day of winter." However in most other languages -- and even in older discussions in English -- the solstices have names like "Midsummer's Day" and "Midwinter's Day."

Is there some sound reason (e.g. typical temperatures, asymmetrical sunrise/sunset times, thermal inertia, etc.) to consider a solstice as the first day of a new season, rather than the middle? 

Also (perhaps less on-topic) is there any record of when the change in nomenclature took place in the U.S.? Are there similar discrepancies in other English-speaking countries or in other cultures?
There are three main ways to reckon seasons:

Solar. The 3 months with the greatest insolation are designated summer, so the solstices and equinoxes fall in the middle of the season. In the Celtic calendar, summer started on 1 May; in the traditional Chinese calendar it is 5-7 May. The cultural 'Midsummer' and 'Midwinter' festivals reflect this.
Astronomical. The solstices and equinoxes are the starts of the seasons, with summer starting on about 21 June (it varies). Its use dates back at least to the Romans, and it's used in most western cultures today (apparently not in Russia, Australia, or New Zealand).
Meteorological. This is what professional meteorologists use (e.g. UK Met Office), and is based on the prevailing weather on land at mid-latitudes. Seasons are 3 months long and summer starts on 1 June.

I've tried to illustrate the relationships with insolation and temperature here:

There are some other ways too:

Ecological. Scientists who study the behaviour of organisms (hibernation, blooming, etc.) adapt to the local climate, sometimes using 6 seasons in temperature zones, or only 2 in polar and tropical ones.
Agricultural. This would centre around the growing season and therefore, in North America and Europe at least, around frost.
Cultural. What people think of as 'summer', and what they do outdoors (say), generally seems to line up with local weather patterns. In my own experience, there's no need for these seasons to even be 3 month long; When I lived in Calgary, summer was July and August (hiking), and winter was December to March (skiing). Here's another example of a 6-season system, and a 3-season system, from the Aboriginal people of Australia, all based on weather.

Why do systems with later season starting dates prevail today? Perhaps because at mid-latitudes, the seasonal lag means that the start of seasonal weather is weeks later than the start of the 'insolation' period. In a system with no heat capacity, there would be no lag. In systems with high heat capacity, like the marine environment, the lag may be several months (Ibid.). Here's what the lag looks like in three mid-latitude cities:

The exact same effect happens on a diurnal (daily) basis too — the warmest part of the day is often not midday (or 1 pm in summer). As with the seasons, there are lots of other factors too, but the principle is the same.
These aren't mutually exclusive ways of looking at it — there's clearly lots of overlap here. Cultural notions of season are surely rooted in astronomy, weather, and agriculture.