While it's pretty clear from your question what method you're talking about, the title isn't so clear. When I hear factoring by grouping, I think of something like $3x^2+2x+9x+6$, and not $3x^2+11x+6$. When the student has to first come up with a way to split the middle term I've heard it called, not surprisingly, factoring by "splitting the middle term" and also "the AC method".
As for the AC method, I agree with Dave L Renfro's comment that one reason for teaching certain things is to reinforce basic skills. A little practice with some mental arithmetic is never a bad thing, although I guess they'd get that with pattern matching too. AC also includes what I would call factoring by grouping in the final steps, so that gets practiced as well. I've personally taught the method before because I had the time and freedom to do so, and because I think it's a cool method. However, if I had to choose between AC and, say, completing the square, I think I'd teach completing the square every time. AC is nice but omitting it is no big deal.
For what I would call factoring by grouping, as in my first example $3x^2+2x+9x+6$, I would want all students to be able to factor this by inspection. There's at least one major result down the road that it's very useful for: proving the product rule by writing $$f(x+h)g(x+h)-f(x)g(x)=f(x+h)g(x+h)-f(x+h)g(x)+f(x+h)g(x)-f(x)g(x)$$
which is itself a great example of proof by "hey this term might be helpful to have so I'll just jam it in there and make up for it elsewhere to keep the equality". (Another great example is completing the square, which doesn't have as much of a rabbit out of a hat feel as the product rule.)