Bookkeeping uses a different reasoning system than you are accustom. I think of it as vectors in a 2-dimensional space (asset/liability, income/expense) -- where each vector has a magnitude and a direction (debit/credit). You can think of "debit" being the head of the vector (where value is going), and the "credit" as being the tail (where it comes from). Transactions are paired, complementary movements in this space -- not plus/minus movement along a single line.
Visually, it's much easier to distinguish between a debit and a credit if they are in different columns. A tiny little minus sign won't do it. Of course, you could use color, but, that's not always printable. Parenthesis are OK, but, it makes sanity checks in your head difficult. Of course you could do this transformation a report if you wanted, but really, how often does that happen?
Logically, these are actually very different activities. When you debit an asset account, it's representing a kind-of-activity that happens (retained value accumulating). Once you view credit/debit as just plus/minus, you're tempted to neglect the other dimensions of the interaction. To a beginner, debit/credit affect on asset/liability/expense/income accounts seem like an unnecessary distiction, however, the interactions are inverted in their affect. Is minus good or bad? It completely depends upon your perspective.
Redundancy is a feature not a defect; it's a checksum. There's always a tendency to simplify the model and elminate the balancing interaction and check. This is possible, of course, and it does simplify the recordkeeping. However, it means that logical classification errors are harder to discover. When (perhaps big) money is at stake, why take the risk? By having 2 complementary transitions in a more complex space, you cause the person making the entry to think... and that's very useful (even if it's tedious or exhausting).
Pratically, you have convention/tradition. You're making a choice to use plus/minus for credit/debit is one of the distinctions, you could just have easily use it for asset/liability or income/expense. Why favor credit/debit? While this may not be the best way to solve these concerns, the approach is the incumbant -- most financial people expect this kind of problem to be this way, regardless of the extra complexity involved. Tradition here reduces communication overhead.
Even so, the rules arn't passed down unwittingly, they form an approach known to work. I think each generation is welcome to challenge (and they often do challenge) tradition, however, new approaches need significant justification.