Although I agree with the interruption part, I think it's sometimes worth cutting people who interrupt you a bit of slack as some people tend to talk more when they get nervous.
For example, if you start explaining your fantastic plan for what we can build in 3 days, but I know we have a 1 day budget.
It’s unlikely that they are delivering a 10 minute monologue without ever offering a pause to let you politely and naturally interject with your information.
More than that though, the idea that you have no need to listen to what they are saying - because you know what it is and is likely a waste of everyone’s time - tells me that you are probably a terrible listener and likely a difficult person to have a conversation with.
In the example you give, by shutting them up, you basically have shut the door on any good ideas they might have - ideas that might be good regardless of the time budget.
You cannot predict what someone is about to say, ever. You can make guesses, and sometimes you’ll be right, but the worst case of “I know what you’re going to say so let me cut you off” being wrong is far, far worse, than letting it play through and being right.
In the former case, you reinforce that this person will simply stop talking to you or telling you stories because they think you are rude. In the latter case, you’ve wasted a few minutes of time but continue developing a relationship and building trust with which you can ask clarifying questions without coming off as rude and alienating your conversation partner.
If someone starts with “here’s what we can do in 3 days” and you know only 1 day is available, that’s the perfect moment to spend 10 seconds correcting an assumption. No incorrect predictions necessary.
As someone who usually does not like to be interrupted, I would have no problem being interrupted this way. I prefer being understood as I speak so I can clarify and possibly adapt as we speak.
On that note, asking a clarifying question in the form of a statement of your current understanding of something is IME the best way to come to an understanding of complex discussion.
My brain is a stack, and most people are queues, so if I don’t write it down, I have already forgotten it; but that’s only really important for interruptions that lead to tangents.
Interrupts from an active, engaged listener are usually received positively.
It isn’t easy, but it’s possible, and over time it does get easier.