My guess is if there wasn't a Lighthouse score, the focus would be on another singular metric instead, like First Contentful Paint for web performance. The score, while imperfect, helps at least to have a focus on something that weighs multiple metrics.
As an industry, I'm wary of having a single company define these scores. It seems like a conflict of interest. I'd rather have this in control by a standards group.
My issue with the score is that it is numerical. If I get 91, I want 100.
Having a traffic light style system whereby green is good, red is bad etc. would give a decent target without the costly Uber optimisation for perfection.
To your point of a single company defining these scores - a standards body would be great, I agree, but there's a danger it'll be like all the other web standards bodies, whereby Google is a member, albeit one with pretty much all the power.
As an industry, I'm wary of having a single company define these scores. It seems like a conflict of interest. I'd rather have this in control by a standards group.