They wouldn't licence the design.
Then, a competitor (I don't recall who made the first VHS decks) came around, and outsold them. Sony, rather than letting it continue, dumped BETA.
We've had at least 5 BETA decks that I can think of. 3-4 Sony, 1 Toshiba. Until we got our first VHS, we had 2 BETAs hooked into the TV at all times.
But, back on topic again, my family has:
2 copies of the OT movies on BETA (some older taped-off-TV ones, plus some backups of the Faces edition)
(Although I don't remember ever seeing it, my parents told me they used to have a bootleg of ANH, but the quality was so bad, they taped over it.)
Faces Edition on VHS, non-widescreen
Special Edition on VHS, widescreen*
TPM VHS, widescreen, special box set*
TPM DVD*
AOTC DVD*
*- What I own, others belong to my parents