In some cases the information about the microstate elements is more important or the macrostate variables suffice. Eg with $\Omega(E,N,V)$, for the microcanonical, because you assume that the aggregate 'de-labeled' effect on the system is all that you need. Consider the Ising model where the configurations over the lattice do not matter, only the aggregate total, $H(\sigma)$. You could say that if there are particular spatial arrangements that would matter, but you assume they don't.
A particular case is when there are microstates which are inaccessible, eg. some patterns are not feasible for whatever reason. You may look at the number of macrostate $(E,N,V)$ and say that not all of the number of $\Omega(E,N,V)$ are possible.
A silly example; imagine you are tossing a coin and are scared of large consistent sequences of heads (H) or tails (T) (inspired from Hamlet), you toss it 5 times, and as a rule you do not throw a 5th trial if the rest were all of the same random variable outcome from fear. So, -HHHH*- and -TTTT*- prevent the set of $R={HHHHH,HHHHT,TTTTT,TTTTH}$ from being realized but a sequence such as $THHHH$ is feasible to be seen because it is known that the 5 consecutive trials is no longer possible although in terms of the macrostate there are a member of $R$ which has the same macrostate; therefore making it inaccessible. So it would have to be looked not just at the macrostate level.
So the macrostate size for $\Omega(five same)=0$ (none accessible), and $\Omega(foursame)=8$ (partial accessible for this macrostate).
Tracking individual particles in the case of an ideal gas is not typically considered and ignored usually by default.