No it's not. Not only cursive writing, any form of writing is not important to learn. A person with his own style of writing is better then a person forcefully trying to learning any other form. But there is one more thing important that writing should clear and legible. Like we keep ourselves neat and clean to look smart and gentle man same we should also have neat an clean so we could look well educated and knowledgeable person. And I want to give example of my brother like he used to write in very good writing but his teacher used to scold him and forcefully made him to write in cursive form after sometime by this thing his writing became poor and now he neither uses the old form nor the cursive form and that's the bad effect of forcefully changing his writing in cursive form. So by my opinion cursive (or any other) form of writing is not important to learn.
You just need to improve your own form of writing and that will be the best option for anyone.