I don't have time for an in-depth history, but you can't talk about stage antics without talking about Jerry Lee Lewis. Just watch this video from beginning to end and you'll see exactly what I mean. He was famous for his erratic, manic behavior on stage; he would play with his feet, stand on the instrument, and even was rumored to have set a piano on fire (Source). Here's how one biographer describes his performances:

Jerry Lee loads up the song with his signature moves—the egocentric first-person references, the theatrically raised arms, the absurd glissandos, the pounding double-time right hand, the long blond hair threatening to burst loose from the pomade..." Source

I am assuming that by "stage antics", you are referring to the idea of spectacle (pyrotechnics, lighting, lasers) as well as performance (singer performing in a cage!, crazy props! dancing girls!)?

Part of the reason for stage antics has to be the fact that post-1965 (Beatles at Shea Stadium), bands began playing larger venues. Smaller, intimate venues allow audiences to take it all in aurally and visually, but a 4-piece band on a giant stage in a stadium with limited amplification of the times meant the stage had to be livened up.

The then underground acid rock movement of 1966-1968 was heavily influenced by Surrealism, film, avant-grade art and the idea of "art as performance". They were among the earliest group of musicians who forged the aesthetic of combining music with lighting, images, performance and text. Early Pink Floyd, Jefferson Airplane, Grateful Dead were important contributors to that aesthetic.

By the early 1970s, we also had the emergence of Prog-Rock and heavy metal and artists like Alice Cooper took to employing outrageous costumes, props (boa constrictor, guillotines and even stating a hanging) and turned rock music into full-blown theatre. ("This is Spinal Tap" beautifully skewers this in the film with those Stonehenges...)

(Of course, by mid-late 1970s, the backlash against "spectacle rock" had begun in full earnest with Punk.)

Many stage antics emerged from London in the mid 1960s. The Who under the influence of their manager Kit Lambert, finished their sets by apparently smashing their instruments. Much of this was stagecraft, with prop guitars switched in at the last minute.
Jimi Hendrix arrived in London in 1966 armed with all the gimmicks guitarists used on the touring circuit of the Southern states for the couple of minutes they had when the lead artist introduced the band members, such as playing the guitar behind his head. Under the influence of The Who he began setting fire to his guitar.
The Who and Hendrix took their acts to The Monterey Festival in 1967, and the film made of the event carried the antics way beyond the original audience.
Simultaneously the arrival of LSD in London gave rise to light shows. Pink Floyd a musically indifferent band made their mark on the early psychedelic scene with a light show they had developed with the landlord of a couple of the members who taught at Hornsey College of Art. Pyschedelic light shows were further developed by the artists Mark Boyle and Joan Hills at the UFO club of Tottenham Court Road, first with Pink Floyd and then with the jazz rock band Soft Machine. Soft Machine together with Boyle and Hills, joined Hendrix's US tour of 1968, taking the techniques they had developed to large stadium audiences.
Source: Jimi Hendrix London by William Saunders (Roaring Forties Press, 2010)