You are
An LCD screen
My predecessor and my component can be stricter than me
The predecessor to LCD screens, Plasma screens, were more "strict" and one had to be careful with them: if you left one picture on the screen for too long, it would burn permanently into the pixels (this is not an issue with LCD screens, however).
I'm used to be read from not a wire, but a wave.
Visible light (which is how humans read LCD screens) is a type of Electromagnetic wave.
You may use me where I'm used, an example is right in front of your eyes.
Most computers and smartphones use LCD screens and that's how you are viewing this.
I am alive, though some parts have died.
LCD screens are still alive and well, but some smartphones (parts of the screen industry) like the Samsung Galaxy S7 and Nexus 6P now use AMOLED screens (not LCD screens), meaning some devices have killed off their use of LCD screens.