I have been using FEA since the 1980s. When I started it was just coming out of "research" areas and it was fairly novel in consulting for heavy industry at a local level. It's now taught as an undergraduate tool. How common is it these days?
FEA has grown beyond manual methods and has embedded within many software applications. We are in a phase where we use FEA software applications to analyse even a simple beam. Considering the industry, still linear model is predominantly used due to the awareness of the linear limit of a material. The industry people need to just identify at which point the material fails as per the yield stress. So, as long as industry is concerned, linear FEA is the first approachable method.