Input - you still have the same connections available. I still perfer a wireless gamepad on any non fps game. You can still dock it with your mouse, keyboard, and monitor. Your already docking it with the eGPU. I would perfer using my TV + wireless game pad instead.
Laptops overheart unless they are sitting open and must be sitting on a table not a carpet lest their bottom fans get blocked and again, overheat.
So its pretty awkward to find a position to properly plug them into your nice big gaming keyboard, mouse, and display. If you are using the native display then an extra keyboard and mouse sit too far from the screen and are again awkward to use.
Using the built in laptop keyboard is not as good as using a real keyboard.
Output - You always have HDMI allowing you to use your kitted out home theater setup.Which should be far greater (>>>>>) then the pc setup.
Home Theater PC.
Flexible - Yes parts are interchangeable, but you can only go so far since standards are always changing. Buy what you want once, and change up every generation or so. Just like with the desktop.
It costs an arm and a leg to get it from manufacturer and the components are sub par (eg, 16GB of RAM and top end SSD).
Also, I can't fit an OS SSD and a RAID array of 3.5" HDD into a laptop (aka, its less flexible due to size restrictions).
Also AFAIK laptops typically limit you to 2 slots for ram (and small slots at that) rather then 4 or 6 large slots on PC.
And of course, GPU... no way to fit a good one into laptop...
However, eGPU will provide such a way which would greatly improve flexibility of a laptop.