While a noble pursuit, I think there are dozens of start-ups (completely free/open apps as well as for-profit businesses) trying to do exactly this. I think Trello counts as a big one.
Actually it's related to my laziness (and hopefully others had that too) to write to-do list because of these two things :
1. It will become a long list (when reaching 10 or more items) and it made me psychologically "lazy" to write more or mark some item as "done".
2. I just realised that it's best to focus on one thing and make it done as soon as possible rather than seeing a long to-do list.