There's nothing particular about strong acids or strong bases that disqualifies them from being a primary standard, but most of them are too unstable or difficult to work with to be useful as a primary standard. A primary standard should have these qualities:
High purity
Stability in presence of air
Absence of any water of hydration which might vary with changing humidity and temperature.
Cheap
Dissolves readily to produce stable solutions in solvent of choice
A larger rather than smaller molar mass
Now for the examples you gave:
$\ce{H2SO4}$ is hygroscopic, so it's concentration will change quite readily in air.
$\ce{HNO3}$ is very hygroscopic as well. The $\ce{NO3-}$ anions can also start redoxing other things which isn't particularly useful for titrations.
$\ce{HCl}$ is a gas, so it will be difficult to determine the concentration of the solutions (you'd have to compare it against another primary standard), and high-concentration solutions are unstable.
$\ce{NaOH}$ is hygroscopic as well.
As Georg pointed out below, one generally needs high-purity solid compounds so they can be weighed accurately (and in addition to the cons above, these substances are difficult to find/weigh in solid form). I hope this helps.