There are only 2 that will do this, today() and now() and the difference is
that now includes the time as well. The date function does not update unless
any of the previous function are part of it.
You can also use Ctrl + ; to get the computer date.
The computer doesn't not know what today is, anyone can change the date on a
computer, you are asking the function to get the time and date from the
clock in the computer. What if the clock in wrong, how are you going to
update that if you have several hundreds of linked formulas dependant on
this. This is not doable. There are no functions that work this way, all
functions update if the source changes. If the contents of a cell changes
from 0 to 100 a formula dependant on that cell will change as well but you
are asking that a function will only update once.
What if you mistakenly cleared what was in A12, 3 weeks 25 minutes and 14
seconds after the formula was originally created, that would mean your
function would stop working since it would return a blank, now you would put
back the non zero value but the formula would update with the current  date
and time?
That is not possible unless you use circular referencing like in the example
or the better by using an event macro as in the example as well.