Initially, it was going to be only desktop, because we were targeting big enterprises who still rely solely on phone for customer service. So, pretty backward companies. A Desktop app would have been perfect and not too "revolutionary".
But, then, we decided to not limit ourselves to that market alone, and have since made the transition to include web and even mobile solutions.
My advice is to: Stop hesitating. Write code (MVP?). Run private and open betas. Collect feedback. Make predictions. Make decisions. Maybe your market will rejoice over your desktop app and maybe they won't. The point is, you won't find out until you actually test it. If it works then that's great. Now, you can focus on marketing and growth. But if the feedback that you get points that your customers would rather get web, then that's also great. Because, now, you've gained an important insight about your customers, and will have a choice of either to switch to web (if it's a true market need (also from customer feedback)) or to start something new.
TLDR: Based on our market research alone, you CAN definitely make a living off of a desktop application; it depends on your customers, that's why it's paramount that real customers test your app asap. Don't worry about the future too much. If your desktop app is successful and somewhere along the line, customers demand a web app instead, you can always scale and adapt.