My supposition has been that, absent Apple to throw their weight behind the iPhone, someone would have created a pure touchscreen device (Android had one such concept under development IIRC) but it would have failed because it would have been just one phone among many, gathering dust at retail stores.
Apple bet the farm on one phone, had the built-in fan base to leverage, and the resources to make it work well from day one.
Though it was a factor -- it's real success was that it was OS X in a tiny phone -- basically a portable Mac with totally wireless connectivity. For many applications you could simply leave your laptop at home and walk on the bus and go on with your day.
Steve Jobs even said at its launch that the iPhone rans OS X and ran "desktop class applications". This with it's multi-touch full screen keyboard and GUI integration meant that people could interact with it much more naturally than any phone in the past. Even my mother could use it, which is remarkable, considering how many cell phones I gave her that she couldn't use.
I guarantee you that the most used features from day one of the iPhone launch were: Safari, Google Maps, and YouTube, with the Music app being simple a "nice to have".
Apple bet the farm on one phone, had the built-in fan base to leverage, and the resources to make it work well from day one.