Old-School British Accents Were More American, Less British
Fun bit of linguistics here: Shakespearean English had an accent closer to American English than modern day British English.
But it’s actually the opposite: at the time shortly post-Shakespeare and pre-Ichabod when the majority of British settlers arrived in North America, they actually spoke much more like current Americans than current Brits. One example is in the pronunciation of R after a vowel: at this time, everyone on both sides of the Atlantic was saying things like “paRk youR caR in HaRvaRd YaRd” (well, if cars had existed at the time, which they didn’t. Harvard Yard actually did exist, which, just…whatever, Harvard Yard).
We can tell that the rhotic pronunciation was the original one for a couple of reasons. For one thing, there has to be some reason why we write an R in those words in the first place, and basically everything that seems illogical about English spelling is actually totally reasonable if you go far enough back into the etymology. Another way we can show that people pronounced things in a particular way before we had recording devices to prove it is spelling variation, especially from less-standardized text like private notes and letters or from respelling schemes in early dictionaries. For example, if someone is writing “should” as “shud”, we can be fairly sure that the /l/ is silent for that person; conversely, if people don’t start writing “park” as “pak” until 1775, we can suppose that they didn’t start pronouncing it that way until around the same time.
So anyway, some Brits sailed across the Atlantic, speaking rhotically, and then they rebelled against the mother country, speaking rhotically, and then they founded America, speaking rhotically, and then they decided to make a time-travel action/supernatural TV series featuring some excellent characters of colour, still speaking rhotically. I may have skipped some steps, but speaking rhotically is in every single one of them. (Well, unless you speak one of the American dialects that isn’t rhotic, like Boston English or Southern English, but let’s not complicate things here.)
Meanwhile, back in Ye Olde England, everyone had also been speaking rhotically for quite a long time, but people started getting tired of it in the period just after the American Revolution. (Although we’re not quite sure why: perhaps this was just the 18th century equivalent of memespeak.) The first evidence we have of non-rhotic pronunciation is from a dictionary by John Walker in 1775, and pretty soon thereafter everyone was “pahking theih cahs in Hahvahd Yahd”. Metaphorically speaking. (Well, except for the people who speak a British dialect that is rhotic, like Northern English or Scots, but again let’s not complicate things.)