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.