I think showing the product alone works well only if the investor is in the target audience. I just met with an entrepreneur who has what I believe is a great product, but the investors he has talked with so far are just not going to be users of it.
In his case, I think having a couple of slides to help demonstrate the problem is very helpful. Otherwise there isn't a sufficient aha moment when he gets to the solution.
Certainly the business case is important to lay out, especially in the case you describe. Many decks don't do that though - they don't stand alone without a verbal pitch. They lack context and sometimes even topic headings.
I've seen many decks that have a page with a heading like "Opportunity" and a number (along with the obligatory graph going up and to the right). What is that? Competitor sales? Expected market share? Entire market size? Even if the investor is watching you pitch out loud, they may refer back to the deck and find they have forgotten what you said about that slide.
In his case, I think having a couple of slides to help demonstrate the problem is very helpful. Otherwise there isn't a sufficient aha moment when he gets to the solution.