Why are documents kept separated when training a text classifier? Most of the literature considers text classification as the classification of documents. When using the bag-of-words and Bayesian classification, they usually use the statistic TF-IDF, where TF normalizes the word count with the number of words per document, and IDF focuses on ignoring widely used and thus useless words for this task.
My question is, why they keep the documents separated and create that statistic, if it is possible to merge all documents of the same class? This would have two advantages:

You can just use word counts instead of frequencies, as the documents per class label is 1.

Instead of using IDF, you just select features with enough standard deviation between classes.
Common words should not be ignored.  For instance, there may be a correlation between document classes and whether more indefinite articles like a or an are included or more definite ones like the or this.

Neither is word count is a good substitution for word distribution. (Frequency though it is commonly (not necessarily frequently) used is an incorrect term.  Words do not normally occur periodically in natural language.)  Representing word distribution throughout the concatenated text of multiple documents of a single category.

The distribution of use of individual words and the distribution of language units and word pair proximity may correlate well to document classification, but the linguistic pattern distribution may vary from document to document within the same class, so the distribution of distributions is relevant.  The deviations between distributions is information needed for proper statistical analysis.

In ten documents of differing sizes, the distribution of words may differ for some words and correlate for others.  Concatenating them hides the distribution of distributions.  From an information theory perspective, concatenating and totaling across the concatenation would represent an information loss with respect to separate documents analysis.

The naive Bayesian machinery produces the most reliable categorization when all information is integrated into the probability calculations.