Would you like to memorize the guitar fretboard? Would you like to be a fluid, adaptable guitar player? Ideally, you should be able to play the guitar as easily as if you were humming or whistling. It might take you many years to achieve this goal, or most likely you will be working towards it for the rest of your life, but that could be your goal. Learning the guitar fretboard will help you.
Without knowledge of the guitar fretboard you will have a hard time learning how to improvise on the guitar. You need to know where you are putting your fingers and why. One of the benefits of knowing the notes on the fretboard is that it will help you to make new songs your own. Instead of dumbly following a chord chart or sheet music you will be able to experiment with variations to notes and chords as you learn the song. Also if you learn a riff by ear or from guitar tablature you need to be able to transpose it to any key to suit other musicians you are working with. So the bottom line is if you do not know the guitar fretboard, you are severely limited.
But the fact is there are many, many guitarists who do not know the notes on the guitar fretboard. The reason is that on the face of it, it appears to be a difficult thing to do. If you are studying a keyboard instrument, you memorize one octave and you know them all. It is just a bunch of black and white keys. If you can play a melody on the left hand end of the piano, you can also play it on the right hand end. Learning the keyboard is a walk in the park. So that is your problem in a nutshell: the guitar fretboard lacks an obvious pattern.
The way to remedy this situation is to give the guitar neck your own pattern in the form of whatever scale or chord you are learning at the moment. But we can make it simpler than that. Let us take the notes of the octave as they appear on the guitar beginning at the open sixth string: E F G A B C D. This pattern repeats all the way up the guitar neck. You just need to remember that you jump a whole fret between all the notes except E - F and B - C. So you have the names of the seven notes in the octave. You can play these notes all the way up the guitar by starting at E on the sixth string and going up, and then starting at A on the fifth string and so on.
Now we have the starting point that the guitar neck is not lacking in patterns, it is just that the patterns are not visible like they are on the piano. So now we can begin learning. First, take any note, say C, and find it on the sixth string in the first position, and continue on up the fretboard. Then find and play all the C's on all the strings, working your way up the neck. Now that is about as much brain work as you need - just finding the notes. Do not try to remember them. After a few days of practicing this exercise your mind will have formed its own network of associations to help you remember the positions of the notes. The next step is to find more ways to challenge your memory of the notes. You could, if you are learning to play blues, learn in your head the names of the notes in the blues scale and find where these notes are further up the neck. Or learn the names of the notes in a particular chord and find those notes in different positions.
Your progress in memorizing the notes on the guitar fretboard will depend on your willingness to find more challenges for your memory. The benefits of working on memorizing the notes will be seen within a couple of days but it might take weeks or months before you can say with confidence that you "know the fretboard". The alternative is to be hampered by not knowing the notes on your guitar as is the case with so many guitarists.