PS4 indies are like 360 arcade titles.
360 indie games are like 99 percent unplayable crap made in one night by 10 year olds. They don't have achievements, only a very few are decent to good.
PS4 indies are games like Pinball Arcade and Mercenary Kings. Quality games from real development teams. They have trophies and a professional development quality.
When xbox fans rag on "indie station" I honestly think they are failing to realize these are not the same things. Part of the most important thing on 360 was a constant supply of XBLA games. It's just not realistic to have awesome AAA retail releases every week. I'm lucky if two retail games I want come out in a month. Arcade/Indie games keep me occupied in between these spaces. Some of 360's best games were Arcade titles and in the end of the PS4's life I'm willing to bet it will have been the same situation.
I just don't honestly understand how anyone can so easily dismiss having so many extra games available regardless of your console of choice. If they don't appeal to you that's fine but that doesn't mean they don't appeal to other people.