it's probably not that complicated to see if people will use a free service or not.
certainly it's more complicated and expensive to try to determine ridership changes on say one bus route if the price increases 25 cents.
One of the big challenges with determining uptake for a free service though is getting firm and true commitments. It's incredibly easy to say yes to something free, because there's no barrier to entry. But in practice, for every 10 people that say they will use a free service, probably only a handful will actually use it.
It's like getting people to register for a free event. It's a fruitless effort because you'll probably get 100 people to register, and then 40 of them will not attend because there's no disincentive to not show up. But it's really easy to say yes, because you might go and it's free, so why not register. But then look at a paid event, of the 100 that pay the registration fee, you'll probably get 90-95 showing up because they've made that financial commitment to attend...if they don't show, they lose something.
So if you did a study on how many people would use a free service, you'd get incredibly skewed numbers because a ton of people would just say yes for the sake of saying yes, even though they may never intend on using the service.
I'm sure most of us have things we get for free that we have every intention of using but just never do, because there's really no disincentive to not use that thing.