In standard American English, dinner always refers to the main meal of the day. In traditional agrarian contexts, the meals were breakfast, dinner, and a light later meal called supper. Supper is related to the word soup and is therefore similar in connotation to the North English/Scottish use of tea to refer to a later light meal by the name of one of its (potential) components.

The shift over time from breakfast, dinner, and supper to breakfast, lunch, and dinner primarily reflects changing socioeconomic realities rather than some fundamental lexical shift.

Fairly well-off family in the Ozarks, USA. We only say "dinner" when it's a special occasion and it isn't in the morning. For normal meals it's breakfast, lunch, supper. Most of my classmates in elementary school (many of whom had not enjoyed those "changing socioeconomic realities") were the same.

I feel like you're conflating "traditional agrarian" with "rural." I also feel like you're conflating "changing socioeconomic realities" with "people getting rich or well-off."

Was your elementary school in a one-room schoolhouse? Did most people go home for the mid-day meal? Was school in session through the summer and winter with breaks for the planting season and the harvest? Did most people stop going after 6th, 7th, or 8th grade? If not, then I feel like your post may be non-responsive to mine.

Yes I probably misunderstood you, because I have no idea what you meant by "standard American English". I'm an American and I speak English, and my rural neighbors are the same, so I thought I would report my observations. Around here we rarely use the word "dinner" for meals eaten in one's own home.

I think breakfast/dinner/supper was standard usage among my extended family in Alabama -- I have to say "was" because I haven't been there since the early 1970s, but I wouldn't be surprised if it hadn't changed.