Grummans are well built. The company built warbirds, and these are built about the same way - sturdy.
Just because a company with the same name built warbirds doesn’t make the AA1 or AA5 sturdy or good.
They’re very simple in construction, which lent itself to the original intent of its designer well. I personally feel that simplicity also gave them a cheaply constructed feel.
Regardless of construction techniques, I see no reason why one couldn’t be used for primary training. The biggest hassle will probably be finding an instructor that has enough Grumman time to meet insurance requirements.