Time series forecasting dilemma. Could feature engineering overcome time dependency?
They all start from the same assumption: time series forecasting can't be treated as a regression/classification problem. It is time dependent, which means our target y at time t depends on what the value y was at t-1.

Time series forecasting must take into account time dependency, but it doesn't have to be the only source of information. Many complex forecasting tasks take into account external variables and time dependency altogether.


What prevents me to use some basic feature engineering and transform
the example data as follow?
| timestamp | value_at_t_minus_7 | day_of_week | value |

Nothing prevents you from doing that. Moreover, that value_at_t_minus_7 is time dependency. day_of_week can also be thought as a simplification, or summarization of time dependency information - because studying seasonality we concluded that x can be explained with the value of one week ago. It's another way to make time explain the output.
When working with regressions (such as ARIMA or Tree-based models) you have to manually specify what is the shape of time dependency. Therefore the method you proposed is perfectly &quot;legal&quot; and actually very common. Good luck with your task.