The Nebuses of his day would have had exactly your attitude towards da Vinci that you do towards the possiblities of human sensory powers beyond the accepted five.
Scientific progress does not get made by the wise orthodox sitting somewhere saying "It cannot be." Scientific progress is made by the rebel, the questioner of orthodoxy asking "Can it be?"
And by giving the evidence. Provide the phenomenon that shows it. Provide the explanation grounded in well-accepted theories that implies it. Provide the experiment that would, if done right, show the thing, or refute it.
Psychic abilities would be expected to provide an enormous evolutionary advantage; they should be widespread. They have been seriously sought after by scientific methods that should be suitable to find something for nearly a century now. Nothing has turned up. One can make excuses to explain this while supposing psychic powers to still exist. But the supposition that they do not exist fits all available observed repeatable phenomena and all generally accepted theories. There are some things that just aren't so, however fun they might be to imagine.