Cheer!, ─ You are very Solomonic, and you learn quite fast/well, but how is it called in English (American): “TANSTAAFL”.
If the CO2(g) from CaCO3 doesn’t leave the System, then also all the CO2(g) you picked up during hydrolysis, during dilution, and during titration will not leave the System either.
In such case you will find a too small value of H2SO4, now simulating a too high content of Aspirin!
You can’t make a method more specific as it is by its nature, ─ You have to live with.
(But you can combine/change methods!)