A chat on your homepage could answer every visitor who turns up with a question, in your voice, at any hour. Most companies do not put one there, and the reason is not the cost. It is one wrong answer. A chat that invents a return policy or quotes a price you never set has cost you the customer who believed it.
Every reply comes from your own material. Your help articles, your pages, your posts, your documentation. Not from what a model knows about companies like yours.
Every reply also carries its sources. A visitor can open the article the answer came from, and so can you, which matters the first time somebody asks why the chat said something.
When a visitor asks about something your published material does not cover, it tells them so.
That decision is made before the model is asked to write anything, so a thin match cannot turn into a confident paragraph.
Not everything you hand the platform is something it may quote as your claim. Your own pricing is a fact, and the chat gives a visitor the number. A competitor's pricing is context, so it shapes how the chat positions you and never appears in front of your customer as your price.
It writes in your brand voice rather than a model's default, out of the same voice the rest of the platform writes from. A question asked in French comes back in French.
Somebody opens it, asks what they came to ask, and gets an answer without making an account. The conversation stays with their browser, so they can close the tab and pick it up later.
You have already written everything it knows. That is the whole cost of putting it on your site.
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