Your explanation is actually incorrect on why Beta failed. Firstly this was not a story about Sony vs JVC et al, it was about Sony vs Universal Studios. Universal was so irate and fearful when Sony won the court battle, they foot the R&D bill for Victor to develop a new format under the condition they shared it with everyone with very low licencing fees.
At the time, Universal made more than 50% of the movies and would not allow any of their movies to be on Beta. Betamax died because of lack of content being squeezed out by Universal. It was because of that, Sony went into the movie business so in future they could control content as well as they do today.
If you think the Blu-ray vs HD DVD was similar, well no, it was the same! Sony vs Universal again, this time Sony owned their own content and had enough clout to fight and win this.
Beta dying had nothing to do with stubbiness, or pride, or recording times or anything like that. It was Sony's intent to mostly use Betamax as a TV recorder, Universal turned it into the home movie concept to protect their interests and reluctantly licensed movies for home watching, that was their "if you can't beat em, join em" solution to the situation and put Betamax out of business for spite.