The premise that visible business failure harms brands is false. It's your opinion and it sounds like it makes sense, but it's not supported by any data.
Given that many forms of visible business failure literally cause brands to cease to exist, it seems indisputable that at least some of the time they're harmed.
"Some of the times they're not" does not exclude a potential correlation.
For example: "Some of the time, going to the hospital will not make me better, therefore there is no correlation between going to a hospital and getting better"
We may just have to disagree on the value of Google. It seems obvious to me that it is a critical asset to Alphabet that must not lose search/product share before another Alphabet subsidiary pays off. I believe the purpose of spinning companies out of Google is more about improving capital allocation than protecting either brand, with the possible exception of Waymo if there is a huge backlash against autonomous vehicles.
That sounds like an interesting study, where can I read it?
Maybe, but it's a popular belief in business anyway; moreover, however true or false it is in general, I think it's pretty clear that Google, specifically, has a problem (whether rational or not) in some potential customer sectors with service/product discontinuations reflecting negatively on perception of other services/products under the Google brand, even if that is a sui generis effect rather than a reflection of a generally-applicable effect of product failure on brand image.