"It is correct to use commas in dialogue tags," said Dan, taking another bite of cheesecake.
Note, however, you don't need a comma in cases like this:
"I need to work out more," says the guy stuffing cake into his mouth.
where the entire phrase is identifying the speaker via the action.
Here are some additional links that discuss this:
(Just to make sure we address the heart of the matter: You mentioned you're reprinting an old book; I'm presuming that's just incidental, and you're not asking because you're considering whether to alter the original punctuation, yes?)
Generally speaking, there is nothing stylistically wrong with such commas. There are two things in play here:
- Punctuation exists to make reading more clear.
- Punctuation can alter the meaning of a statement.
As to the first point, it's uncommon to encounter a situation where there would be any ambiguity if you didn't include a comma after the speaker. (Plus, if such a sentence were that convoluted to begin, then the writer might be better off rewriting it altogether.) So in this one regard, you might see commas in this situation as superfluous.
However, this isn't necessarily the sole purpose of these commas. Even ignoring the possibility of long, confusing said-so-and-so statements, there can't (or shouldn't) be any blanket statement that such commas are an "outdated style," because punctuation also alters meaning. Writers use punctuation to tweak phrases exactly the way they want them to be read.
Commas, in particular, affect pacing, as though taking a breath while speaking. They can influence how the reader interprets the timing of an action in very subtle ways, slowing down or speeding up a statement. This is just another tool writers have to fine-tune their writing.
In many cases, it may make no real difference in meaning whether the comma is there or not. But to summarily dismiss all cases of this usage as antiquated is misguided.