Not only should Trek and sci fi be pausible, it should be inspirational. Science fiction often leads to science fact as it inspires the scientists, engineers, philanthropists, and other doers to make the future they see and read about happen.
Look at how much real modern technology was inspired by Star trek. One wonders what the state of technology like cell phones would be like if Star trek hadn't inspired engineers to create them.
When the writers use their creativity to postulate the possibilities and make their stories believable, it may inspire someone to think those realities are within their reach.