I am about at the end of my PhD* (a few months left) and my supervisor's advice still rings true: try to keep the feedback loops short. If you have to spend months figuring out if something is worth doing, then it becomes rather risky to try. However, if you can shorten the cycle from idea to rough confirmation down to a week or two, then you can afford to explore the options.

The trick is of course that there are several ways to approach this: you can develop more flexible tools, become more independent in the lab (if you have lab work), learn more theory, learn more tools, buy more compute power, pick easy problems etc.

Another angle I have thought about (and learned the hard way), is that there is a big difference between research and development. My topic is closely related to engineering and thus it is sometimes attractive to want to "solve a problem". Unfortunately, many measures of "good research" supposes a relevant application, but "solving a problem" is much more difficult than "understanding a problem". The understanding truly has to come first.

Also, these two pieces of advice (Short learning feedback; focus on understanding not solving), are not guarantees to produce "groundbreaking" research. In the end, the most important product of a PhD education is you and the skills you develop.

* A PhD in Denmark is a bit special, in that it is very short (essentially limited to 3 years) and thus has a slightly different scope.