For a time series problem, Why is it preferrable to use a time series model over a model without an explicit time component? High Level Question:
What is the advantage of modeling data as time series?
For a problem involving (mutlivarate) time series data, why is it useful to model the problem as a time series problem, 
time       | value1 | value2
-----------|--------------
2020-01-01 | 1      | 3
2020-01-02 | 2      | 3
2020-01-03 | 3      | 1
...        | ...    | ...

instead of a classical tabular format?
day of the month | month | year | value1 | value2
01               | 01    | 2020 | 1      | 3     
02               | 01    | 2020 | 2      | 3
03               | 01    | 2020 | 3      | 1

So, when I want to foreacast my time series, for the time series approach I would use a model as ARIMA or RNNs. 
For the "classical" format, I would use something like a linear regression or a decision tree. 
Why would you prefer the time series model?
My assumption:
you take into account autocorrelation and give more weight to "more recent" observations. It also consinders the ordering.
But wouldnt the "classical" model catch these relations as well? but with a combinaiton of the three variables? 
What is the main reason to use a time series model? Intiutively, this is clear to me. But I cannot really explain it.
Can anyone help me clarify this
 A: Superficially, the time series approach is more convenient mathematically, whereas the human date is more convenient for presenting the data/results.
On a deeper level, as you correctly noted, one could use day, month and year as three independent variables, particularly, especially if there are reasons to think that there are periodic variations (e.g., seasonal or related to the cycle of the solar activity). Whether it improves or worsens the things depends a) on the method used to analyze the time series (is it capable of capturing periodic movements on the scale of a year or several years?) and on the amount of data (more variables means more parameters, so this increase the risk of overfitting.)
A: Yes, in principle your "classical" approaches would catch periodicities and autocorrelations as well. Fitting an AR time series model is not that much different from OLS regressing the actuals on lagged values of the actuals, after all. However:


*

*Suppose you run a standard linear regression with day, month and year as predictors. Your regression will not understand that a predictor setting (1, 3, 2020) is very similar to (29, 2, 2020). Yes, the third predictor is identical, but the other two are not, and the difference in the fit will be $28\hat{\beta}_{\text{Day}}+\hat{\beta}_{\text{Month}}$. Compare this to the difference in the fits for a predictor setting of (28, 2, 2020) versus (29, 2, 2020), which is just $\hat{\beta}_{\text{Day}}$, although the two pairs of predictor settings are both spaced just one day apart.
Also, regression has no idea of autoregression.
Of course, you can hand-craft your regression, by including a day counter to account for the first fact above, and lagged values of the outcome to account for autoregression. But this will be a lot of work, and it will actually not be mathematically optimal.

*Now suppose you look at a decision tree, or possibly a Random Forest. Yes, this should be able to learn interactions between predictors, like the difference between (1, 3, 2020) and (29, 2, 2020) above. However, it will need a lot of data to do so. Much more than if you just used a time series approach.
Bottom line: you can either use a specific tool for the job (time series analysis), or adapt other tools (regression with a lot of predictor adaptation), or use very general tools that will then require a lot of data (CARTs and Random Forests).
A: If you think that the impact of X on y changes over time regression will not work (well, OLS won't). Autocorrelation is another problem inherent in time series data although special SE have been developed to address that. If Y influences itself over time then linear regression (non-time series) is not going to work correctly either I believe. 
