While there's a lot to be said for buying physical games, either because you're a collector or you like the option of being able to trade your games in to fund the next purchase, exclusively downloadable software is most likely the future we're heading toward. However, it isn't a new technology. If you look back through the annals of gaming history, you'll find a number of antiquated hardware systems that offered downloadable software as an option and by and large they all worked and only really differed in their availability and hardware. There was the Nintendo Satellaview that offered exclusive titles for the Super Nintendo (some of which have been the subject of admirable preservation efforts); and there was a similar service offered by Sega in the form of the Sega Channel. There are earlier examples still, and you can find a rudimentary run down of some of them here.
The Dreamcast too, offered such a service and it was called Dream Library. Unlike the aforementioned utilities though, Dream Library didn't offer Dreamcast games for download; instead it offered Japanese gamers the option to use their Dreamcast as an emulation device with which to download and play a selection of Mega Drive and PC Engine games right in their browser. Similarities with Nintendo's popular Virtual Console are quite apparent, but Dream Library precedes Virtual Console by six years, give or take; and the main difference is that games were rented temporarily with Dream Library, rather than bought outright.
A fairly short-lived service, Dream Library ran from June 2000 to January 2003, and it did suffer from a few technical issues that meant it wasn't as perfect as it probably initially sounds. Still, it was quite an ingenious service and another example of Sega's thinking outside the box when it came to pushing the Dreamcast as a jack of all trades. Not only was Sega pushing its hardware as a gaming machine, but also a business machine, an affordable alternative to a web browsing computer and also an emulation device. I'm still wondering how the console failed to crack the mainstream during its natural lifespan, but as usual I'm digressing.