Are math grad students increasingly consulting SE and Wiki, ignoring research librarians and libraries, to their own detriment?
I think wikipedia is good for mathematics topics that are fairly settled. There are few errors and the ones that do appear (I've found some) tend to disappear quickly. You can get a good overview and if you follow up on the sources provided you can get a more complete view. So, I hope students use this for background on things they need to study.
But, by its nature, it is less useful to bring you to the state of the art: stuff that isn't yet &quot;settled&quot;.
I think SE is the opposite, in some ways. You  might find answers to contemporary questions, but the sources may be less reliable. Wikipedia has many editors (formal and informal) keeping things right, SE, less so and not everyone commenting really has a good answer. So, again, I hope that grad students use it when necessary, but with caution.
If the alternative is to set for ten hours at a time in a library, pulling older and older books from the shelves, it is no contest.
But reading things and being given answers isn't the best way to gaining insight into a mathematics problem. Not deep insight, anyway. For that you need to do some work yourself.
And, as you say yourself, it is a professional approach to use such resources. You do it yourself. And, I would say &quot;to the detriment&quot;, actually. It is a supplement and/or a place to start.