Is it not possible to compile the original source code (of course cross compilation for the required hardware etc.) of android and directly install on the smartphone? Why there are tons of ROMs available on the internet? If I just want the vanilla android, is it possible to install it ?
If someone has taken the drivers from your device's code, added them to the AOSP android code, and successfully built it then yes.
You have a lot of ROMs because each devices' hardware requires different drivers to run the display and various chips. Moreover, the manufacturers want to customize the look and feel of Android and add their own features.
And then you have 3rd party projects like CyanogenMod, which focus of providing extra features.