What usability issues occur with an application form only showing one question at a time?

My client is thinking about having an application form, with approximately 25 questions. The type of questions will be personal information such as name, date of birth, address, as well as financial questions, current living arrangements and so on.

They have an idea to make the website look high-tech by only producing one field at a time. They haven't explicitly stated, but I pressumed they could want a 'next' button to view the next field.

Other than the user not knowing how long the form is without some kind of breadcrumb/trail/visual indication, what other usability issues occur with this kind of design?

Is the conventional form structure (all question on one page or a group of questions split out in sections) on a site the best way to gather this information?

And has there been any popular/mainstream sites that use this technique for gathering information? I myself have never seen it, so I want to discourage the client from going with this approach.

I have visited this page Forms? One question at a time or the whole form on one page? but this question is regarding command line, which mine is not. I can also see someone has said as long as it's no longer than 5 questions, but I wanted to know if there was more science/studies to show this, and does this apply to on a browser?