Endless games as a feature is good, but not as a limitation. This means, if you have a endless mode as an extra option, then all good, but if you only have endless mode, then that's a limitation, and imho, a game with endless mode only takes away a key element of an enjoyable game: Feeling of accomplishment.
If the game is amazing, you may be able to get away without it, but a story with an ending and then go infinite gameplay usually is preferred.
If a story takes too long to develop, then a simple solution is just to make gameplay achievements.
I've only made a few 'endless' games myself. There's a certain appeal to them. Minecraft Beta, the long drive, Yumme Nikki, tower defense games. Games that you can play forever and never really quit.
but there is also a huge difference in design philosophy there that doesn't apply so well to games with more of a story focus, which is where I usually work. Both ideas are great, just different types of feeling you get from them.
