Well I wasn't around for it but I believe the main reason why it failed to gain popularity was Sony tried to control everything about it, especially not allowing porn on it, while VHS supporters did, and fully licensed the format to various companies that made cheaper recorders.
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This is not true. It is based on a misunderstanding of the TV world in the mid-1970's.
TV in the mid-1970's was dominated by broadcast TV. People used their VCRs to record broadcast TV shows for later viewing. Every generation of VHS had twice the recording time of Beta. This allowed a viewer to record an entire week of her favorite soap opera on a single cassette. This was not possible on Beta.
VHS was supported by RCA (a huge consumer electronics company), Matsushita (Panasonic, Quasar,
etc.), JVC, and many others. Beta's supporters included Sony, Zenith, Sears, and a few others. They were no slouches, but Beta's supporters were not nearly as big or as many as VHS supporters.
Beta was a favorite among engineers, but its strength on the test bench did not translate into the viewing experience. As I stated above, the VCR was used primarily to record broadcast TV. At 220-240 lines or resolution, broadcast TV do not display the strength of Beta.
The prerecorded cassette market developed later. Movie prices went from below $50 to more than $100. Porn producers jumped into this market in a major way and dominated it almost until the prerecorded cassette market peaked. They sold product on both Beta and VHS until it was clear that the Beta market was going nowhere. The video rental market rose as a consequence of the $100+ video cassette.
NV Philips developed the 12-inch Laser Disc as a high-end alternative to the video cassette. It wanted its disc to display educational material, opera, and big-time movies. It refused to allow porn. Nobody bought LD. NV Philips loosen its porn restrictions to allow somewhat sexier material, but it was too little too late.
It is a shame that so many people today try to compare the Blu-ray/HD-DVD dispute to the VHS/Beta dispute. The World is very different today than it was 30 years ago. The two contests have little in common.