The status bar was put there for a reason, and both Apple and Android guidelines discourage designers from hiding it.
Apple:
Think twice before permanently hiding the status bar. Because the
status bar is transparent, it’s not usually necessary to hide it.
Permanently hiding the status bar means that users must switch away
from your app to read the time or to find out whether they have a
Wi-Fi connection.
With Android this used to be stated more explicitly, but they still say that:
The system bars are screen areas dedicated to the display of
notifications, communication of device status, and device navigation.
Typically the system bars (which consist of the status and navigation
bars, as shown in figure 1) are displayed concurrently with your app.
Apps that display immersive content, such as movies or images, can
temporarily dim the system bar icons for a less distracting
experience, or temporarily hide the bars for a fully immersive
experience.
If you're familiar with the Android Design Guide, you know the
importance of designing your apps to conform to standard Android UI
guidelines and usage patterns. You should carefully consider your
users' needs and expectations before modifying the system bars, since
they give users a standard way of navigating a device and viewing its
status.
It's best to follow the official platform guidelines. They do both allow hiding these bars, but they suggest to only do this with immersive apps. In other words, you shouldn't be looking for reasons to display the status bar ("is it important for users to know the time"), but rather you should assume that it best be displayed, unless you can find a compelling reason to hide it (e.g. "it's crucial that the app gets the undivided attention of the user").
BTW, with regard to important stuff located in the status bar - the time and signal strength may not be as important as incoming notifications and especially the battery level.