I think it's important to check for dependence because
1) the statistical properties of the things being estimated depend on that.
For example, standard errors will generally be affected by the presence of autocorrelation
Autocorrelation is an obvious form of dependence to check for in a time series.
2) as you note, if there's dependence structure in the residuals this implies there's unexploited information that could be used to improve the model.
how come others do not check it in the papers
Well, I can't detect everyone's thinking, but I'll explain one factor that I think is important:
Many of the people doing ANN and Support Vector regression (and many other things besides) come from areas outside statistics, and not all of them are used to the notion that their inference is affected by dependence structure (indeed, the very notion of statistical inference is not always familiar to everyone - which is why stuff invented by statisticians decades ago turns up in some other area, under a new name quite regularly - but we sometimes occasionally return the favor).
I've encountered exactly the same phenomenon in other areas too - including seeing one person fit a model to cumulated numbers that essentially suggested that for much of the data, the implied covariance between the current cumulative and the next observation was around and maybe even smaller than minus the product of their standard deviations (though the estimates of those things may not have been consistent - and yes, the impossibility of that should have been a clue there was a problem somewhere, if he'd understood what he was doing enough to try to calculate its implied value). The actual correlation in the values (given suitable models) was near zero but slightly positive (as would be expected if you understood the process).
He was used to simply using least squares on any problem involving estimation and that's what he'd done, but he wasn't even aware of the implications of any dependence structure, so when he cumulated things that were already positively dependent and then started fitting nonlinear curves by least squares to the result, the rest of his inference (and forecasting) was pretty meaningless without taking all that into account.
Things like this happen more often than I care to contemplate.