Desktop/laptop keyboards utilize shortcut via key combinations like Ctrl + V.
What don't mobile keyboards, like on Android and iOS, do this?
If we implement shortcut keys in mobile applications will it be added benefit to the user or it will cause headache to the user?
In general, it is useful to have shortcuts on desktops because you are use the keyboard anyway. On a smartphone or tablet on the other hand, you are not continuously using a keyboard.
Therefore, you would need to open the keyboard, to be able to do certain actions, which would simply result in an extra step for the user in the process (opening the keyboard, before actually doing what they wanted to do).
Shortcuts exist to make things easier, it shouldn't make things more complicated. There are shortcuts on both iOS and Andriod, they simply work in a different fashion, a more logical fashion when you don't have a keyboard.
The shortcuts on computers exist because you have (at least) two different ways of interacting with your user interface, namely using a keyboard, and using a mouse / touch-pad. In order to switch from one to the other, you have to move your hand(s) to use the other method. Also the mouse requires precision to use correctly, something which may be difficult for some people. Users may — if they are familiar with the shortcuts — use the computer more efficiently by using shortcuts.
The typical example would be using TAB to step through the elements of a form, something which requires a simple button-press when using shortcuts, but that requires lifting one hand, moving mouse pointer, stopping mouse pointer at the right place, clicking, moving hand back to keyboard when using the mouse.
On a smartphone with touchscreen, you have only one method of interaction: poking at your screen. You never switch back and forth between different methods of input. If anything it would rather make the interface confusing and harder to navigate if every you needed to call up a QWERTY keyboard on the screen to access application.
That said...
Note that you can make shortcuts on a smartphone. This is especially prominent on Android phones where your point of entry of the Home screen, where you have shortcuts, widgets and similar that provide quick access to different functions. And then you have the "Apps" listing, which shows everything.
You also typically have a "search" function (rarely used it seems) where you can access all apps and content directly from the Home Screen after typing just a few letters.
The main reason behind keyboard shortcuts is to make command selections faster. According to Fitts' Law time to point at an object depends on the distance to that object and its size. On a desktop distances between UI elements are bigger and their sizes often smaller compared to mobile versions. On top of that mobile keyboards are initially hidden and keys are small which makes multi-key combinations slow to articulate. For these reasons keyboard shortcuts don't achieve the goal of accelerating selections on mobile. Gestures do.
One extra consideration. Research demonstrates that shortcuts rely on recall rather than recognition. Consequently, they are a more demanding interaction technique, harder to learn, and as such are designed for expert users: those using an app frequently, invoking tens / hundreds of commands in a single session. Only in this case extra effort offsets the cost of memorizing key combinations. So before considering shortcuts it's worth to think about a particular app: is it a tool to be used heavily or something more casual. Looking into objective data would be ideal.
Why don't mobile devices utilise keyboard shortcuts? They do! I'm using a device that does that right now. It's called a BlackBerry. While it doesn't have shortcuts for copy and paste (because there are only the letter keys, which are being used to type, and no control keys), in non text-entry situations such as reading email, shortcuts abound. 'I' and 'O' to zoom in and out of a website, 'R' to reply or 'F' to forward an email, 'C' to compose a message, 'U' to open the calculator... you get the picture. There are hundreds of keyboard shortcuts spread across the OS. But BlackBerries have keyboards, which is something that no other phone has.
Which gives you your answer. Desktop computing devices have keyboard shortcuts because there are always multiple forms of input, as other answers have stated. Laptop and desktop PCs have a keyboard, mouse, and sometimes a touch screen, and each of those input forms can be used simultaneously. Android and iPhone phones, however, only have the touch screen. While they could technically employ keyboard shortcuts, using them would be awkward and slower than other ways because it would involve manually opening the virtual keyboard, which covers up the content, and it provides no tactile feedback. Because the keyboard is always available on BlackBerries, keyboard shortcuts work just fine.
