The reason is very simple: efficiency. In multiple ways.
Native data types: The closer the data types of a language match the underlying data types of the hardware, the more efficient the language is considered to be. (Not in the sense that your programs will necessarily be efficient, but in the sense that you may, if you really know what you are doing, write code that will run about as efficient as the hardware can run it.) The data types offered by Java correspond to bytes, words, doublewords and quadwords of the most popular hardware out there. That's the most efficient way to go.
Unwarranted overhead on 32-bit systems: If the decision had been made to map everything to a fixed-size 64-bit long, this would have imposed a huge penalty on 32-bit architectures that need considerably more clock cycles to perform a 64-bit operation than a 32-bit operation.
Memory wastefulness: There is a lot of hardware out there that is not too picky about memory alignment, (the Intel x86 and x64 architectures being examples of that,) so an array of 100 bytes on that hardware can occupy only 100 bytes of memory. However, if you do not have a byte anymore, and you have to use a long instead, the same array will occupy an order of magnitude more memory. And byte arrays are very common.
Calculating number sizes: Your notion of determining the size of an integer dynamically depending on how big the number passed in was is too simplistic; there is no single point of "passing in" a number; the calculation of how large a number needs to be has to be performed at runtime, on every single operation that may require a result of a larger size: every time you increment a number, every time you add two numbers, every time you multiply two numbers, etc.
Operations on numbers of different sizes: Subsequently, having numbers of potentially different sizes floating around in memory would complicate all operations: Even in order to simply compare two numbers, the runtime would first have to check whether both numbers to be compared are of the same size, and if not, resize the smaller one to match the size of the larger one.
Operations that require specific operand sizes: Certain bit-wise operations rely on the integer having a specific size. Having no pre-determined specific size, these operations would have to be emulated.
Overhead of polymorphism: Changing the size of a number at runtime essentially means that it has to be polymorphic. This in turn means that it cannot be a fixed-size primitive allocated on the stack, it has to be an object, allocated on the heap. That is terribly inefficient. (Re-read #1 above.)