"But you can't be arsed to make that small investment in yourself before applying for a new job?"
Bills don't pay themselves. Why can't you, the employer, be arsed to make that small investment in your new employee? You're the one with the capital.
"Your job as an engineer entails constantly learning and trying new things in order to find the best solution"
Exactly, job. As in getting paid for it. Not sure why you think it's a duty. A sacrifice that employees must make for you.
"I might as well give the work to a much cheaper coder in an off shore sweatshop."
Enjoy the results. :)