Realistically when you think about it it makes no sense, why would American English be closer to old English than British English?
Standardization of RP only ocurred in the last 200 years.
Although a form of Standard English had been established in the City of London by the end of the 15th century, it did not begin to resemble RP until the late 19th century.
en.wikipedia.org/wiki/Received_Pronunciation
As for the “why,” though, one big factor in the divergence of the accents is rhotacism. The General American accent is rhotic and speakers pronounce the r in words such as hard. The BBC-type British accent is non-rhotic, and speakers don’t pronounce the r, leaving hard sounding more like hahd. Before and during the American Revolution, English people, both in England and in the colonies, mostly spoke with a rhotic accent.
Around the turn of the 18th to 19th century, not long after the Revolution, non-rhotic speech took off in southern England, especially among the upper and upper-middle classes. It was a signifier of class and status. This posh accent was standardized as Received Pronunciation and taught widely by pronunciation tutors to people who wanted to learn to speak fashionably. Because the Received Pronunciation accent was regionally “neutral” and easy to understand, it spread across England and the empire through the armed forces, the civil service, and, later, the BBC.