The public has the interest. If they didn't, they would not be so quick to latch onto so many crackpot speculations mispackaged as "science". It's not a matter of scientists not wanting to be bothered to correct this; we are simply the wrong tool for the job, or at least we need many others to do it right. Look at any product, from something simple like paper towels to something complicated like GPS units or pharmaceuticals. The people who develop and deliver the advertising for these are not the same people who developed and now produce the actual products. They are people with expertise not in science and engineering but rather in economics, marketing, psychology, writing, art, etc. Ideally they work with scientists and engineers to gain a basic understanding of the product, which they can then pass on to the general public. (I realize much of advertising is designed to manipulate rather than pass on genuine information. I am giving it the benefit of the doubt for this exercise, considering it in its idealized form of helping the public become familiar with a "product" so they will understand its benefits.)
And yes, we need to get those who "don't do well at science" to understand some basic level of science, just as we encourage people who are completely non-athletic to maintain some basic level of physical fitness, we expect people with no literary gifts to be able to read and write, and we expect people who will never go into politics or run a business to have a basic understanding of how our government and economy function. It's as simple as that, and as difficult.
While all true in the modern world you're not really looking at whether this is the best solution. I've done sales and the easiest sell is when you want what you are selling. I sold plenty of graphics cards purely in the basis that I wanted a new graphics card. Of course the overwhelming urge to research which one helped enormously but most people don't do their research, they want convenience.
Hence it is with science. They will devour what matches their world view and dismiss all else.
As someone knowledgeable if time slows as you reach light speed and many will nod and say yes. Ask them why and they scratch their heads and give all kinds of weird answers. Not one person has postulated that what the common man considers as time is not that is being measured.
Ask someone without good reading and they have no interest whatsoever. Why then would they bother to research the latest in chemistry? Hell, all the discussion about time travel around films and so few consider it past its story telling applications.
Consider a more polarised example. People buy things like designer handbags. Why? Because they are designer. No one asks what's the extra value or why they should pay more. They accept the world as sold because that is what they are conditioned to do. To question is hard work and they want an easy life. Hence if a paper tells people that immigrants are taking all the best jobs, houses and benefits then scores will adopt it. Few of them ever ask "if ten thousand people move in, how many new jobs are created to look after them?".
The track record is long. A person is a reasoned and thinking being. Capable of compassion and understanding. People are nervous, reactionary and instinctual. Likely to round on anything new and different with great fervour.
As for who to do this feat,there are many instances of the guy with the skills to make the goods being the best guy to sell the goods. Science is no different in this marketplace. It's just another commodity.
Of course you could remove the sales side by cooperation but that muddies the water on Nobel prizes and new grants. If you're going to be competitive, you have to play the game. If you're not then you have to find another way of funding what you're doing.
