Let me ask you a few questions about your post, if you do not mind:
1) Fragmentation - If you buy a new Nexus 4, 7 or 10 sold directly from and supported directly by Google where you get the latest OS updates directly from Google, how does fragmentation effect you?
2) If you customize any OS to the point of it not being useful, how is that the OS's fault? Isn't that the users fault for not knowing exactly what they want? Why would anyone customize to the point that its useless? Wouldn't you stop once you reached the point of satisfaction?
3) So, its more productive to say, open the cal app to see your appointments next week, open your reminders app to see your to do list, then open your mail app to see your recent emails, then open your Podcast app to listen to a pod cast, then open your music app to listen to music, of then open Pages to look at a document...of and you want to know the weather, then go to notification center, and press the date to OPEN THE WEATHER APP...
Isn't it nicer to have all that information, assuming that is important to you, on a screen or two, nicely summarized and then, if needed open the related app to work with the data, instead of opening apps only to decide if you need to do something?
The above are just examples; but you get the idea; I could go on and on how widgets make the OS far more productive over opening apps over and over again.