If you get a lot of value from something you pay nothing for, and it doesn't increase your job output in dollars and cents, then there's no reason it should increase GDP.
The funny thing is, Google basically enables my job. Good luck searching even on StackOverflow without it. Of course I could program without it, but it wouldn't be the same kind of programming, the projects wouldn't be the same, they wouldn't move that fast. Google is an excellent engine for browsing distributed documentation (i.e. all those random webpages detailing how to use the thing XYZ you need).
If we're talking about how good the economy is, I'd argue that we should count all the good (and bad) that the economy is doing, not just the GDP.
These are indirect costs, but they still have an overall economic effect.
You could argue - perhaps with some justification - that the net value generated by Google search is more than the net economic costs. That would be an interesting thing to try to estimate, and so far as I know no one has attempted it.
But that just highlights the underlying problem, which is that most mainstream economic models are completely unfit for purpose.
We're trying to run a 21st century economy using banking systems that haven't changed in principle since the 15th century, and econometrics that have barely evolved since the 19th century.
And all of that happens with a huge political bias that overestimates the value of some activities - including speculation, and other forms of wealth capture - and underestimates the value of authentic wealth generation.
In fact no one knows how well the economy is doing, because we barely have any idea what an economy is - certainly not in 21st century terms, where "the economy" is clearly a global pattern of resource flows, innovation, and future potential, not just an epiphenomenon of national or corporate accounting.
Not calculating GDP correctly is a tiny symptom of that. A full solution is probably going to need a complete reinvention of the entire field.
GDP increases are nice, but they are by no means the only important thing to consider. many other considerations must be made when creating or changing public policy.
> something you pay nothing for
So, obviously, yes, if you buy ice cream GDP will go up.
Take Linux + Apache, for example. I can create a business for very little money because those are available to me for free. But are they only economically valuable when they cost money? If I used Windows to create my business instead, that would contribute to GDP, even if my business failed. Two (not perfectly) equivalent products, but one counts as GDP, and the other doesn't. Once you see that "economics" can contain more than dollars, then you see that GDP isn't the correct measure of economic activity.
And if you do, that business shows up in the GDP.
What's the commercial value of a free live streaming app that captures evidence of a (say, for the sake of argument) a police assault, which eventually leads to a riot?
GDP is like a summary of all relevant execution paths through code. But it's really a list of paths that are considered relevant for traditional reasons.
It's not a complete picture, and in many ways it isn't even a useful one - because there's a huge implicit social morality tied up in econometrics that makes assumptions about social value.
Those assumptions are becoming less and less relevant for all kinds of technological, political, and even economic reasons.
[0] - a thing that nicely differentiates those who understand math fundamentals from those who don't - realizing that all theorems have a set of assumptions behind them, and are not valid outside that assumptions
Clean your own house - no GDP.
Pay someone to clean your house - GDP.
Same amount of work is being done, but GDP only counts what is paid for.