Java: Why am I required to initialize a primitive local variable?

Because it's a local variable. This is why nothing is assigned to it :

Local variables are slightly different; the compiler never assigns a default value to an uninitialized local variable. If you cannot initialize your local variable where it is declared, make sure to assign it a value before you attempt to use it. Accessing an uninitialized local variable will result in a compile-time error.

Edit: Why does Java raise this compilation error ? If we look at the IdentifierExpression.java class file, we will find this block :

...
if (field.isLocal()) {
            LocalMember local = (LocalMember)field;
            if (local.scopeNumber < ctx.frameNumber && !local.isFinal()) {
                env.error(where, "invalid.uplevel", id);
            }
            if (!vset.testVar(local.number)) {
                env.error(where, "var.not.initialized", id);
                vset.addVar(local.number);
            }
            local.readcount++;
        }
...

As stated (if (!vset.testVar(local.number)) {), the JDK checks (with testVar) if the variable is assigned (Vset's source code where we can find testVar code). If not, it raises the error var.not.initialized from a properties file :

...
javac.err.var.not.initialized=\
    Variable {0} may not have been initialized.
...

Source

In fact, the compiler does not assign a default value to your float f, because in this case it is a local variable -- and not a field:

Local variables are slightly different; the compiler never assigns a default value to an uninitialized local variable. If you cannot initialize your local variable where it is declared, make sure to assign it a value before you attempt to use it. Accessing an uninitialized local variable will result in a compile-time error.