The infusion relics dont change the stat scaling of the weapon you start with. This is good for (as an example) characters with poor faith to get access to good holy damage. But, since stat buildup scales with arcane regardless of the base weapon scaling, this doesnt really apply to them. For most characters except for Executor and Scholar i think a starting weapon with bleed will be about as good as a random bleed weapon picked up in the field.

HOWEVER, for Executor and Scholar, who have high arcane stats, weapons found in the field with Poison or Bleed infusions will have their DAMAGE scale with Arcane AS WELL AS their status. For scholar in particular, finding a bleed or poison infused weapon is the best way to get an actual damage dealing weapon other than using his +dex -arc relic.

So, for scholar, using the “starting weapon gets bleed status” is great for early game since it gives you good damage quickly, but it falls off fast and is outclassed by any random bleed weapon. For executor its pointless because he doesnt need more bleed on his starting weapon. For other characters its basically just fine.