I agree that the home screen is sacred space. I've tried my best to organize my phone for maximum efficiency, and have reserved the home screen for my most essential apps, putting the most essential ones on the lower right, in easy reach of my thumb. My phone features:

* Folders for productivity, reference, audio/video, financial, shopping, news and travel/transit apps.
* Clock (native iPhone)
* Calendar (native iPhone - I like the dynamic day/date display)
* Google Maps
* Cozi (family calendar)
* Weather Underground (best weather app I've found that's free)
* Google
* Fitbit
* Evernote
* Photos (default iPhone)
* Notes (default iPhone - since iOS 10 I've been using this more and more)
* Waze
* Kindle
* Pocket
* Day One
* Safari
* Overcast

On the bottom row I have Things (best productivity app I've found, though I agree the perfect one is a Holy Grail), Mail (default iPhone), iMessage and Phone (yeah, I still use my phone for phone calls).

Subsequent pages have settings, storage and utility apps that I use only occasionally.

I'm also a heavy user of the native Reminders app. Thanks to Siri, I don't need to keep that on my home page.

New apps have to meet a very high bar of usability and usefulness. Plus, I'm always mindful of storage restrictions. I try out only a few and keep even fewer.