That doesn't really matter if all you're doing is measuring the relative change in GDP though, and the amount of activity that doesn't register on GDP isn't increasing.

In other words, if you assume non-GDP activity is constant, then GDP does genuinely and accurately reflect economic growth.

Indeed, this is one reason why economists recommend GDP as a useful measure of growth in a country year-over-year, but not for comparing different countries' GDP directly -- the ratio of activity not counted as GDP may be quite different between countries.

Now, if you think that a massive social transformation is underway of non-GDP-registering activities to GDP-registering activities -- e.g. people used to care for their grandmas, now all those people have gotten jobs to pay for care assistants to do it instead -- then yes GDP will show "false growth" in productivity.

But that really doesn't seem to be a major factor. We really are seeing massive amounts of innovation in the economy that improve people's lives. Economists don't just look at GDP -- they look at lots of measures that all tell the same story. Productivity really is going up. GDP growth may not be 100.00% accurate, but it is mostly.