You're close.
Productivity, classically i.e. 'stuff per labour input' - would be a good measure.
But productivity is ultimately measured in profits. If Nike is able to capture massive surpluses by changing their logo and making it more hip, it's deemed more 'productive' effectively, even though it really isn't in the classical sense. I guess you could argue their 'cool logo' does improve people's lives but that's different than the difference between a 'good shoe' and a crap, 1960's one.
And for services, which make up much of the economy? It's hard to measure.
And yes, rent-seeking is the other side, but probably 'the best' companies are 'rent-seekers' in some way, using their value chain power or entrenchment to generate profits. But how much is due to their innovation vs. power is really hard to tell.
Like the AppStore debacle ... what if Apple subsidized the iPhone distribution to recoup profits in their AppStore monopoly? What if if the judge rules they have to open up their AppStore to competition, thereby meaning they have to jack up iPhone prices? Would consumers win in the end? Hard to tell. (Of course, Apple makes a lot of money on iPhones, I'm just stretching reality to provide an example)
One way to do it would be to measure aggregate consumer surplus, but we don't or can't do that.