Many times, markets and business dictate time pressure. So yes, this is very real in startups at least. Like for instance, an inevitable market development might want you to ship code by the next week, however improbable or impossible. I know I'll get a lot of flak for saying this, but that's ok. I've experienced it first hand. In an early stage startup, when faced with the choice of losing revenue/delivering on time, you'll choose the latter. That means your shipping slot is fixed and so are your features. You'll just have to slog it out or work real smart. Even if you cut features, you'll still realize there's a lot to be accomplished in a short span of time. This is mostly a one off thing. If such events repeat endlessly, that is classic bad management. So you'll need to deliver on time, sometimes :).

So, I guess that companies which administer such time based tests foresee at least one such situation for that role. I'm just speculating.

That's more indicative of poor management and planning on the company's side than reflecting on the performance of the candidate if the time pressure is a regular occurrence.

Few people perform well under pressure. Do you want to test what is their mediocre performance under time limits like on a school test or what they are really capable of?

With this approach you will hire people able to churn out crappy but "good enough" code in the limited time. Not people who actually can do quality work.