Personally I think all LI powered devices should automatically turn off charging when full and stay off until unplugged and plugged in again, but no that would be the intelligent thing to do and we'll have none of that! However there are charge alarm apps to the rescue. I use one called simply "charge alarm". At 100 percent the alarm goes off and I unplug my phone right of way. The alarm also sounds when the charge hits 20 percent so I know to plug it in. Both min and max settings are configureable to your preference. I highly recommend this type of app.
The reason that it is not this way is because these devices run off of the battery, not the charger.
The charger only charges the battery.
That is why you cannot run a phone from a charger alone if there is no battery installed.
(Actually, it is sort of possible, but usually ecceedingly difficult.)
What needs to happen is that devices charge the battery and then switch to running from the charger.
Of course, this would mean that they (or we) would need to provide much better chargers than what we use now.
So it most likely is a combination of a few cost cutting measures (better chargers and phone tech added) and planned obsolecence, where the device must be replaced when the battery is dead.
Like
@Hadron says, try not to run it dead. (Your device will shut itself off before you technically hurt the battery, but if your battery is already aged, this can still kill it off.)
The newer devices have very good 'overcharging' protection, both in the phones and the batteries themselves.
So, not long ago, there was a 'scare' about leaving your device on charge for too long, after it is fully charged.
At that period of time, I used my devices as I liked- ran them down more than I wanted and whenever available they were on charge, sometimes for days on end.
I still got 2+ years out of the batteries, and this is within the 'normal' range- although at the lower end of it.
Those devices said something in the manuals about not charging them after 100% was reached.
My new ones both say not to worry about it.
(I wonder if they just want the batteries to wear faster?)
Anyway, as long as you get 2 or more years out of a battery, you are getting the expected life- and with that, I would not go out of my way to change my charging habits.
Life is too short- both for us and these devices- to fret about this thing.