A relevant issue I see is that
for which answers could be trivially Googled
is hard to define and harder to make universal enough. As others have pointed out, both here and on the main Meta, the search engine I use may be unavailable to the OP, or to other readers; the results they get may be different from the results I get; the results may change in the future; some of the top results may contain bad advice; the material in most search results is not reviewed. Other points could probably be added to this list.
A second point concerns the scope of Stack Exchange: as stated on the tour page,
we're working together to build a library of detailed answers to every question about <site topic>
I am not being unable to find any primary source, but "library" and "every" have apparently been part of Stack Overflow/Stack Exchange's mission since the beginning. Meaning that on-topic, answerable questions are welcome here, regardless of the answers they have elsewhere.
Some discussion on the subject has happened on U&L Meta, too. Michael Mrozek's answer, positively received, states that:
All questions are welcome, even if they're easily googled, since future searchers will find us instead of whatever's on Google now, and hopefully our answer is more helpful
A special case may be the questions that happen to simply be really trivial, which are likely a subset of the questions search engines find lots of answers to. A "General Reference" close reason was proposed, but the idea was abandoned out of a too high potential for abuse. Regardless of whether we consider trivial questions an issue, it seems unlikely that new features will be introduced to address it.
As a personal note, among the results search engines show me, other things equal, I tend to prefer those that point to Stack Exchange sites. On average, they are less likely to exist solely for making money from advertising, they tend to have more useful comments and warnings and, despite the scoring system being far from perfect, they have a score.