For the most part, only the very best, most talented people were able to be in a recording studio back then, both as performers, or as facilitators.
The very best of what was recorded then is what is now played as an example of the era.
Ricky Nelson was done in LA using the best session musicians, in the best facilities. Pretty sure his final vocals were overdubbed. For one BIG thing, James Burton lived in the Nelson home, and was the guitarist (at 18 yrs old).
Ben E. King (formerly of The Drifters) was recorded in NYC, again using great session musicians in great facilities.
In both cases, virtually no "processing" was done to the sounds, just great mics (Ricky sang on a U47) through a simple desk, to the recorder.
(Couldn't open the third youtube, it is prohibited outside US).
Today, anyone who wants to can record the pile of garbage of their choice.