My daughter's 3YO preschool teacher told me that my daughter was highly gifted. It took a long time for that to sink in. I figured she told everyone that! Anyway, I never really saw the need to have my kids tested. What would a number do for me? My daughter received all the available services through school, so testing wasn't going to bring in any more.
I finally had both of my kids tested when I thought about sending them to a gifted school, and it was required. I learned alot about the way each of my children learn and their strengths and weaknesses. It was useful for me, though not in identifying that they were gifted, I already knew that.
Honestly, I think the preschool teachers assessment was the best thing for me - I spent the time to figure out what my daughter needed in the way of education. I evaluated all the school options in our area and determine that the public school was in fact the best option. I advocated for (and got, hurray!) additional services for all high functioning kids at various different grade levels in our school system. My husband and I agreed on what we wished for our children. (A chance to be children, to run and jump and play and experience, not just to learn through books.)
The key in my mind is not early testing, but early identification. And the hesitancy is that if an educator (or a pediatrician) identifies a child as gifted and it turns out that the child does not do well in school, then what? Is it incumbant upon the school to ensure that the child achieves at the anticipated level or at grade level... Blah, blah, blah.
I have always said in our district that you should identify the children at preschool screening who are precocious, and label them as such. Then provide services for "precocious children" until such a time you as the school system is comfortable identifying them as "gifted." So perhaps you provide precocious K-2nd graders with advanced reading, and math and explorations options and then at 3rd grade you provide gifted classes or pull-outs or whatever.