ALGOL 68 had "=" for equality and ":=" for assignment, like ALGOL 60.

Therefore the operation with assignment operators were like "+:=".

The initial syntax of C was indeed weird and it was caused by the way how their original parser in their first C compiler happened to be written and rewritten, the later form of the assignment operators was closer to their source from ALGOL 68.

The "natural inverse" relationship between "address-of" and indirect addressing is only partial.

You can apply the "*" operator as many times you want, but applying "address-of" twice is meaningless.

Moreover, in complex expressions it is common to mix the indirection operator with array indexing and with structure member selection, and all these 3 postfix operators can appear an unlimited number of times in an expression.

Writing such addressing expressions in C is extremely cumbersome, because they require a great number of parentheses levels and it is still difficult to see which is the order in which they are applied.

With a postfix indirection operator no parentheses are needed and all addressing operators are executed in the order in which they are written.

So it is beyond reasonable doubt that a prefix "*" is a mistake.

The only reason why they have chosen "*" as prefix in C, which they later regretted, was because it seemed easier to define the expressions "*++p" and "*p++" to have the desired order of evaluation.

There is no other use case where a prefix "*" simplifies anything and for the postfix and prefix increment and decrement it would have been possible to find other ways to avoid parentheses and even if they were used with parentheses that would still have been simpler than when you have to mix "*" with array indexing and with structure member selection. Moreover, the use of "++" and "--" with pointers was only a workaround for a dumb compiler, which could not determine by itself whether it should access an array using indices or pointers. Normally there should be no need to expose such an implementation detail in a high-level language, the compiler should choose the addressing modes that are optimal for the target CPU, not the programmer. On some CPUs, including the Intel/AMD CPUs, accessing arrays by incrementing pointers, like in the old C programs, is usually worse than accessing the arrays through indices (because on such CPUs the loop counter can be reused as an index register, regardless of the order in which the array is accessed, including for accessing multiple arrays, avoiding the use of extra registers and reducing the number of executed instructions).

With a postfix "*", the operator "->" would have been superfluous. It has been added to C only to avoid some of the most frequent cases when a prefix "*" leads to ugly syntax.