For Relevancy: I do not believe that namespaces solve this problem, as 
__autoload does not work with namespaces (and, for obvious reasons, 
shouldn't).

What you are referring to is a utility class.
It only has static members and a private constructor, which should never be 
called (even from the class itself).

Your suggestion could be useful, because implementing private empty constructors 
is just boilerplate code.
PS. Some people even throw an exception inside the private constructor.

One note:
PHP allows calling static methods on class instances and this actually works faster* than pure static call. Compare:

for (... many times ...) {
    UtilityClass::staticMethod();
}

vs

$instance = new UtilityClass();
for (... many times ...) {
    $instance->staticMethod();
}

Creating an instance of a utility class is a neat optimization in heavy loops.

Do not consider me an advocate of premature optimization, but if g*to was introduced in PHP because generated code may benefit from it, ability to create instances of utility classes should not be prohibited for the same reason. If OP's proposition is implemented, people will flock to it, effectively blocking ability to use the described solution.

____
* 25% less time consumed; tests were performed about a year ago

I think what you're describing is a "final abstract" class, which has been 
suggested I think, though I can't find it in the requests.

So make an abstract class and use a trait to pull in an empty final private 
constructor that triggers an E_USER_ERROR. But this is fighting with the 
developer, and adds an unnecessary layer. The developer will always win. People 
are free to throw a wrench into their own machinery if they want. 

The flavor of the class should have no bearing on the default scope of its 
members. Members need to be declared as the scope they should have. What you're 
suggesting also implies we should be able to make protected and private classes 
(in the global scope).

I'm in support of "final abstract" / "static" classes. Doesn't seem to be a 
reason to disallow this. Some kind of declaration that says "this class is 
inert, you can't instantiate it".

Just a quick addendum, "final abstract" would disallow inheritance, which is what 
abstract classes are for. So "static"/"final static" would be cool.

This feature request requires the RFC process[1], so I'm
suspending this ticket in the meantime.

[1] <https://wiki.php.net/rfc/howto>