I don't have an official solution for you, but I want to make a comment about the reasoning behind the current limitations.
You could argue that calculation fields behave a little counter-intuitively when it comes to using "current time", but there's a good reason for this. It's a little tricky to explain, but bear with me. They key point is that calculation fields are only updated when the data they depend on change. As an example, the calculation
x + y will be updated every time
y changes. Now consider the calculation
Current hour + x. The intent of this calculation is to show
9 + x when the time is between 9:00 and 9:59,
10 + x when the time is between 10:00 and 10:59, etc. The problem is that the calculation will only be updated when
x changes. If
x does not change, then the calculation field will show
whatever the hour was when x last changed + x.
The reason we have to do this is to avoid updating calculation fields all the time. The above calculation would need to be updated every hour, but we could just as well have a calculation
Current second + x, which needed to be updated every second! Keeping such calculations up to date would require an enormous amount of computing resources.
We're working on coming up with a solution that balances flexibility and cost. In the meantime, my best suggestion is to use the API or to set up a "Current time"-app as alluded to in the question.