I heard something very much like that from a CEO, "we're in the software business, not the welfare business". This very same CEO ran the business into the ground, and escaped with a golden parachute that included lifetime medical benefits for two sons. It is also reminiscent of HP CEO Fiorina's statement about Americans right to jobs. Perhaps there is a connection between the attitude and performance.
As for the "feelings" of any particular employee, one might just as legitimately ask how employees "feel" when they lose their jobs because the union demanded wages and benefits the company couldn't afford to pay over the long term.
There is plenty of abuse on all sides.
These days unions are a small player; according to the census bureau, 14% of the workforce belong to unions.
That particular CEO may not have been very good at his job, but he had the philosopy right. GM forgot it was in the car-making business and thought it was in the job-providing and health-insurance business. We all know how that worked out.
However, you are correct in that the other extreme doesn't work well for long, either. Disregarding the needs of your workforce is bad business practice, just as disregarding the repair schedule of your machinery is bad business practice, or disregarding the need to advertise your product effectively is bad business practice, etc. All of these are imputs to the eventual output, which for any business is profit. A smart CEO knows he needs to provide competitive wages and benefits to his workforce in order to produce a profit, so the system balances out in the long run.
You are correct that unions are on the decline, and good riddance. Outside of certain geographic areas and for certain groups of workers, they are, thankfully, no longer a factor.