The voltage put out by the alternator is not what the stop start system is looking at. The battery voltage without help from the alternator is what it’s looking at. Along with whatever load is being put onto the electrical system, such as heating, lights, wipers, air con and so on.
A battery may well start the car well enough under more regular circumstances, such as at the very start of a journey until manually switching the car off. However if the battery isn’t healthy enough to carry out repeated start ups particularly on a short run - then the car will decide not to activate stop start. This is to protect the battery and help keep things running as they should.
This contradicts your theory that it’s a ploy to make money as if they were just looking to do that, they’d design the car to just continually keep doing restarts until the battery can’t take the load anymore and fail.
In most cases the problem is people using cars for ridiculously short journeys which doesn’t charge the battery properly. Journeys where their own two legs or two legs plus two wheels could easily take them, which would further help with CO2, but that’s another subject.
Cars and car batteries like to be used for decent runs, that’s the only problem here.