Indeed, the RSpec team officially states controller specs are now obsolete.
http://rspec.info/blog/2016/07/rspec-3-5-has-been-released/
For new Rails apps: we don’t recommend adding the
rails-controller-testing gem to your application. The official
recommendation of the Rails team and the RSpec core team is to write
request specs instead. Request specs allow you to focus on a single
controller action, but unlike controller tests involve the router, the
middleware stack, and both rack requests and responses. This adds
realism to the test that you are writing, and helps avoid many of the
issues that are common in controller specs. In Rails 5, request specs
are significantly faster than either request or controller specs were
in rails 4, thanks to the work by Eileen Uchitelle1 of the Rails
Committer Team.