PM software tends to include other stuff - like team management, SLA considerations etc. dependencies should be part of any task management system IMHO.
To do lists are what the name implies, a list of things to do.
Once you start adding things like dependencies, etc. to a to do list, it's not really a to do list any more.
If you are going to be that detailed about how you do your tasks, then a traditional Project Management tool (like Microsoft Project) is probably what you need.
Sure it's going to have some extra features you don't want, but nothing is forcing you to use those features, especially if the task management part satisfies your primary needs for dependency tracking, estimate/deadline rollups, etc.
Before I can have friends to dinner, I need to buy the ingredients, but before I buy the ingredients it would be good to print the recipes so I don't need to go back to the store. Also, I need to clean the dining room a bit which involves moving the elephant out of the room and into the garage.
Two little streams with deadlines: move elephant, print recipes today.
I worked on an app like this for a while as well, just arranging everything graphically, but abandoned it as too idiosyncratic....
Work projects have multiple dependencies because they involve often many people, but Agile has been also pushing backward the desire to plan too much in advance.
So the desire is to be able to record a target task, and obscure it (so to speak) behind the preparatory tasks. This is where projects and other things come into play. Project: Make a journal for my sister's wedding anniversary. Tasks: Purchase materials, assemble, hire artist friend to produce neat drawing on cover, distribute for signing by family (both sides). Those end up becoming ordered in some fashion (purchase materials, then the rest), or running in parallel (hire the artist friend and paste it into the produced journal, send out a single sewn signature to family and sew it into the final product, assemble the rest and wait). If you've only recorded the task "purchase materials" you don't have a concept of what follows it (and it remains in your head). This doesn't mean you need to see the following tasks, yet (software can hand them behind the tasks they depend on or by date or similar). But recording them is not a problem.