Why is inactivation of neurotransmitters important?
1) In order to stop the process it was implied in
2) It will be reused
Explaining as comprehensive as possible, some actions will only happen when enough neurotransmitters reach the post-sinaptic membrane. As long as they are there, they stimulate the nerves to transmit action potential.
I will take the simplest example possible: a skeletic muscle contraction.
When your neurotransmiters ( Acetylcholine in this case ) reach the junction between a motor nerve and the muscle ( this is called a neuro-muscular synapse ), it makes the muscle contract. If the neurotransmitter doesnt come back, you won't be able to relax your muscle.
In order to take the neurotransmitter back, it will be decomposed ( in this case, using the Acetylcholinesterase ) and then reabsobed into the presynaptic terminal butons of the neurons ( through endocytosis ). If you wouldn't take it back, you would need to synthesise those neurotransmitters again and again for each time you contract a muscle ( and we don't want that ).
Interesting fact: This is also how many drugs work. They block some neurotransmitters from being reabsorbed so the flow of dopamine/adrenaline etc doesnt stop. Thats why drugs affect your nervous system.