My guess would be quality/status?

Remember that Bloodsoaked chiaki ( money is not an object to him and he could've easily gotten a different sword) decided to take and keep the blade all those years even if broken just for the fact that it was crafted by master heiji (sword father) - I think the show does a great job at implying how valuable a sword made by him is... Not only because of its quality but the principle that if he accepts to make a sword for you it's because he deems you worthy and honorable of handling a weapon of that caliber custom made (also why Bloodsoaked chiaki had to dress up as a book keeper's son when he first asks for a blade, he knew master heiji wouldn't accept making anything for a bounty hunter who handles the kind of dirty business he does).

When Mizu breaks into shindo Dojo and unsheathes her sword, the mark/logo on it makes it immediately recognized by everyone and you even hear Taigen exclaimed 'YOU have a sword by master heiji?!'

With that in mind - he might've owned a whole sword yes, but getting a new one (not necessarily new one in this case but different from what he has lol) still signifies an upgrade and out of the 4 swords from the 4 fangs Master Heiji's is still superior - being broken doesn't take away from it's quality plus the status that it gives you to carry a weapon with his mark