Is it always better to use the whole dataset to train the final model?
Interesting question. I personally haven't seen that for products going into production, but understand the logic. 

Theoretically, the more data your deployed model has seen, the better is should generalise. So if you trained the model on the full set of data you have available, it should generalise better than a model which only saw for example train/val sets (e.g. ~ 90%) from the full data set.

The problem with this (and the reason we split data into train/val/test sets in the first place!) is that we want to be able to make statistical claims as to the accuracy on unseen data. As soon as we re-train a model again on all the data, it is no longer possible to make such claims.

[Edit]

Here is a related question on Cross-Validated, where the accepted answer makes similar points to me and mentions other ways of doing things.



We loop over: 


train a model
assess performance on validation set $\rightarrow$ if satisfactory, go to step 5
change model
go to step 1
assess performance on test set
Present model with test accuracy found in step 5


Eventually, if you manage to get a great score on the test set, you can claim it generalises well.  So the question as to whether re-training on the full dataset will improve performance on future unseen data is not strictly something you can test. Empirical evidence of better performance in other related problem sets would be the only source or guidance at the point in time when you must make the decision.

A sanity check would be to test the final re-trained model again on the original test set; expecting that it scores higher than it ever did when the model only saw the train/val set, because it has actually seen the test set during training. This wouldn't make me feel 100% confident that this final model is superior in all future cases, but at least it is as good as it can be with the given data.

Perhaps there are more rigorous arguments against doing what you say (probably academically motovated), however it does seem appealing for practical applications!