If MATLAB used a different storage variety to store scalars, then all code that handled variables or expressions will need to know about all the different storage formats. For example, if you construct a function, then because the same function might be called with a scalar or a vector for any given argument, MATLAB would need to internally track the different formats, because the function is not going to be able to "see" the variables in the routines the function is being called from in order to generate more specific code.
Yes, I know that C++ can generate more specific code in some cases, using "templates" or "overloaded functions", but the cost of that is that C++ needs to generate one version of the code for every variation actually used. And MATLAB is an interpreter, so which variations are going to be used is generally not going to be known until the statement is reached.
If MATLAB used a different internal storage format for 2 dimensions compared to 3 dimensions compared to 4, etc., then the same kinds of problems as above would occur. But that duplicate code could be eliminated if the internal storage format involved storing the number of dimensions and then the dimensions themselves. Which is what MATLAB already pretty much does.
The arrangement that MATLAB uses also makes it quite fast to "reshape" vectors and arrays -- just a matter of changing the header, leaving the storage alone. Reshaping happens quite a bit in science code, in practice.
I know of one project in which the authors put in more than 5 person-years writing the software in Java "because it is a clean language", only to find that the math algorithms came out much too slow because of all the work copying of array contents) that had to be done in Java to shift representations between dimensions. The authors gave up and rewrote the core in C++, which only had to "cast" the pointers instead of copying the contents. MATLAB's reshape() can effectively act like a pointer "cast" between representation dimensins.
