There is no bad data; there is only poorly interpreted data. Google's data is merely a metric and it's useful from that standpoint.
Attribution models are just that; models. It's nice when we can easily attribute a sale or visitor, but even without that, there are still proven ways to measure lift. Marketing companies have been doing this for years, even before digital.
If you're mathematically inlined, or really bored, take a look at things like Receiver Operating Characteristics (ROC) curves, analysis of variance (ANOVA) or Bayesian statistics. These are tools that have been around for years and can still be used to help determine if a marketing campaign or vendor is having an impact on site visits, phone calls, leads, sales, etc. Granted, to do that kind of analysis by hand is time consuming and unless the person doing it has a data-science background, they risk making the wrong conclusions about the data. But it is possible to get an idea of the impact of marketing efforts, if they are conducted in a controlled way, even without direct attribution models.
As an example of this, one of the projects I am working on now is measuring the impact of radio and TV spots and see what kind of lift is generated from them, and to see if there are specific times or days that have more of an impact. I'm still gathering and analyzing the data, but once I'm finished, I'll write up the methods I used and post the results.