It's up to the author to determine if the tags have a purpose, or they're better omitted. Some points to consider include:
If there are more than two characters on the scene, it can get confusing who is speaking very fast. Oftentimes, naming each character who opens their mouth is a must.
Even when there are only two, it's good practice to include a tag every now and then to make sure the reader doesn't lose track. It can happen easily - we're an inattentive bunch. But denoting the speaker with every single line is generally far from necessary. About every third or fifth line, depending on their length, should be perfectly enough; sometimes even less. (Why not every fourth? Because that would mean it's always the same character who gets them.)
"Alice said" tags are also not the only way to make it clear whose line we're hearing at the moment.
Bob scratched his head. "Yeah I hear you, but what am I supposed to do
about it?"
"I'm sure you'll think of something." Alice poured herself a new cup
of cocoa and calmly took a sip. "You don't want to disappoint me, do you?"
Pairing the line with an action shows who's speaking.
More subtly, you can use the heroes' specific style of speech to help the reader's orientation. If Bob is an informal lad full of "man" and Alice is an old-fashioned sophisticated lady, we aren't too likely to mix them up.
That said, tags aren't only good for making sure we know who is speaking.
Tags and action descriptions provide a kind of visual context, or how should I put it, for the conversation. They help us see the characters and the scene, and remind us we aren't listening to two disembodied voices in a void. Used well, they add flavour and colours and mood. Used badly or too much, they stuff the text with repetitive, irrelevant or boring filler, adding nothing of worth.
They also serve as a break to set the rhythm, flow and pacing of the text to the right speed - if in the proper place in the text. Put in a wrong place, they'll hinder the pace where it should be faster.
And by the way, "said" is actually a fairly invisible word that can be used frequently. Some writers tend to avoid "said" so much they end up creating overly purple prose with their flowery verbs. Don't be too afraid of "said".
The bottom line of it all is, do what works best for your story. Find the right amount of tags, the right places for them, and the right way to phrase them. There isn't really a hard rule.
You absolutely can omit tags. Sometimes it's the good choice to do so. And sometimes it isn't.
If you aren't sure, it may be a good idea to show the draft of your story to a well-read and critical beta-reader.
