I think most companies actually need more generalists (especially for web and mobile). Lots of companies switch between different technology stacks every couple of years. Sometimes you don't even have choice e.g., when a new phone OS becomes popular.

This is different when you are looking for someone to work on one task for a short while. But if you are looking for long term employees you should look for people who are good at adapting to new technologies and have good basic programming skills.