Something I hear constantly: salespeople say they need more leads, then the second one shows up, they want to qualify it down to nothing before they'll even get on the call. Pick a lane.
I'd push back on qualifying hard before the call — especially on video, where nobody's driving anywhere. The real cost of a "bad" lead here is 20 minutes, not a tank of gas and a wasted trip.
Here's the bigger shift I'd make: those three questions work better as things you uncover during the conversation than as a gate before it even starts. "No firm budget yet" doesn't mean unqualified — it often just means nobody's shown them what things actually cost. Same with timeline. That's not disqualifying information, that's the conversation you're supposed to be having.
The way I've always thought about it: once you're actually engaged with a prospect, the quality of your sales process should do the heavy lifting — it should be built to convert at the highest ceiling possible, not filter people out before they've had a real conversation with you.
To your direct question: no, I wouldn't stop a call over answers to those three specifically. I'd only end it if it became clear there's no real project or no way we can help — and that usually surfaces naturally a few minutes in, not from a pre-call screen.