That's dangerous. It is easy to lose track of who said what, especially if several people are talking.
IMO, that depends a lot on how you do the overall thing. Sure, if you have a scene where you literally just have 'A said', 'B said', 'C said', 'A said' with nothing accompanying it, then, sure, it'll be extremely difficult to keep track of that. But I'd say that this is hardly the case for most situations. Unless your characters are really just sitting around a table/standing around and discussing something, there is usually something else going on.
Heck, even
if they are just sitting and standing around while discussing, there are likely gestures and expressions to describe because most people don't just sit/stand stiffly the whole time without moving a single muscle. They will make expressions depending on whether they agree/disagree, move their hands to emphasize some of their points, and show emotions by doing stuff like brushing through their hair, facepalming, or whatever else you can think of. They will likely interact with the things in their vicinity as well like hitting the table, picking stuff up, or putting it down, pointing at things, you name it. They can even interact with other characters by doing more than just speaking through moving or gesturing. Whatever works for the situation, really.
That in combination with splitting up your paragraphs (as in, just one character's utterances per paragraph and starting a new paragraph if somebody else takes over) and utilizing quotation marks (opening and closing ones for one character's part or no closing quotation marks if the same character continues to talk in the next paragraph if we have a longer speech) are enough to show which character is talking even in a setting of a larger group in my opinion. Because the context will make clear who is speaking and to whom if you're doing things right.
Now, I'm not saying you should
always leave out said or any other tagline. But I think that in
many circumstances it really isn't needed and could be omitted without losing information. Let me make up a scene as an example and annotate why I think it works:
X picked up one of the booklets from the shelf in the outermost corner of the tourist information and had a quick glance through it. „Oh, look at this!“ He held the booklet up for Y to see. „There‘s a botanical garden in the Via Fratelli. It‘s open right now.“
For the last part, you could absolutely, alternatively, write:
„Oh, look at this!“ he said and held the booklet up for Y to see.
or – if that‘s more to your liking –
„Oh, look at this!“ he demanded and held the booklet up for Y to see.
but IMO, both convey pretty much the same information as my original example since the context makes clear who is speaking to whom: Since X is the one to pick up the booklet and look through it, it‘s clear that it can only be him who holds it up to show it to Y. Furthermore, this is X‘s paragraph. Nobody else‘s actions should be in there unless they‘re perceived by X. E.g. the scene could continue like this in the same paragraph:
When glancing back, X saw Y roll his eyes but he still went on to wave the booklet in his face, not caring at all that he apparently wasn‘t interested.
We do have Y's actions mentioned but through the lens of what X perceives so, it's still clear that this is all part of what X says and does.
Then, after X's actions and part of the conversation are done, you could switch over to the other side for the continuation of the conversation which would be in another paragraph to signify that this isn't about X anymore but Y now:
Y came over to take a look, his face indicating that he could imagine something better than going to look at rows of plants. „What about it?“
„Well, it looks nice. And like the really informational kind. Here, listen to this: The garden is from the 14th century when some monks or something like that were meditating there. And then it became a botanical garden in the 18th century. They even say it was a cultural center.
I‘d say let‘s go and have a look at it. Anyway, it‘s not far from the tourist information and there are some other things around that we could do as well. How about taking the metro from Cordusio to Cairoli and visit the Castello first and then go over afterward?" He looked up expectantly, clearly having everything planned out in his head already.
The first paragraph is about Y but in the second one X's speech starts since the "What about it?" question is closed at the end. On the other hand, the second and third paragraphs are both said by the same person, X, since there are no closing quotation marks at the end of the second paragraph. Now, you might say it's not a problem only with two people but it'd still be the same if you let a third or even fourth person enter in the next paragraph:
At that time, Z and A returned from the store across the street. Z came over to see what they were talking about and leaned over X's shoulder to take a look at the booklet in his hand as well. His face immediately scrunched up. "A botanical garden? What is this? A school trip? I thought we came here to have some fun!"
A slowly trailed after him. Thanks to Z's yelling, he already knew what was up. "I'd like to go and take a look, actually. If you don't like it, you can go and do something else in the meantime. Or what do you think?" He looked at X and Y who both nodded.
"I'll go with Z then. A botanical garden doesn't sound like something I'd have to see either. Here, this is what I found." Y raised a tourist guide that he had opened in the middle. The current page showed the photo of an aquarium. "It's not far from the castello either so we can go there together and then split up."
Z nodded. "Sounds good. Then in the evening, do we meet up at the castello again, or do we go straight back to the hotel?" He looked at the three of them, not sure what would be better. Taking one station with the metro wasn't a problem but he didn't trust Y with navigating around Milan if the way was any longer than that. He couldn't help but wonder if it wouldn't be better to follow X and A after all. How bad could it be to walk around a botanical garden after all?
Now, this is just a rough draft that I made up on the fly. With a bit more time invested in it, you could make it even more obvious but I think even like this, it is already clear who is talking at which point because the parts of the conversation they have are always tied in with what they are doing at the same time.
Maybe it could help to have the 'said'-part in those instances where their part of the dialog starts at the beginning of the paragraph to make it easier to see. But the thing is: You'd get the information only marginally sooner. And if you look at parts like this:
"I'll go with Z then. A botanical garden doesn't sound like something I'd have to see either. Here, this is what I found." Y raised a tourist guide that he had opened in the middle.
there isn't even a difference between going 'Y said ...' and 'Y raised a tourist guide' because you get the information that it is Y talking here at exactly the same point, namely right after his part in the dialog ends. If it was somebody else who raised the tourist guide to show the others what he was talking about, that action should be in the next paragraph to signify that this is another character now.
So I would maintain that there is no big difference between not using the taglines and using them with said included. It really just depends on what you prefer and what fits better with your writing style. If you are not big on describing the situation with who does what or maybe you have a scene where you want things to go extremely fast so it's really just 'A said', 'B said', 'C said', then yeah, it's better to include them for convenience's sake. For a scene where you have the time to add in the context, I'd say it's not necessary though.
Also: The argument for 'said' is most of the time 'it's invisible' compared to other verbs. Now, why add something invisible? Might as well leave it out when it's not needed then and it'd still be just as invisible or actually even more so because, well, it's not there. As long as the context clues make the same information available, you don't really
need 'said', is all I'm saying.