*If the comparison WERE

You are doing a loose comparison between two different types. PHP has to pick a 
type for it. In this case it does 0 == (int)'TEST' and casting 'TEST' to an int 
is obviously going to give you 0. This is what you are going to want in most 
cases. eg. 12 == "12 " (with an extra space there). Chances are the "12 " came 
from user input since everything that comes from either the browser or your 
backend database comes to you as strings, you are going to want that comparison 
to work. If you cast both to strings instead they wouldn't.

If you don't want PHP to guess, use ===

I know the use of ===. The supposed 'bug' that I think exists, is comparing 0 to a non-empty String with double ==

My concern is because:
Observation 1: null, 0, "0", and "" all result as FALSE.
Observation 2: BUT... "A STRING" evaluates as TRUE.  
SO...
0 == "" makes sense
BUT...
0 == "A NON-EMPTY STRING" makes no sense. IMHO False would be the right answer.

Take a little time to examine this:

if( 0 ) echo "0 works as TRUE<br>"; else echo "0 works as false <br>";
if( "TEST") echo "'TEST' works as TRUE<br>"; else echo "'TEST' works as false <br>";

if( 0 == 'TEST') echo "But 0 == 'TEST' belies the statements above!";

Conclusion:
The exact analysis above done in javascript says I am right.
I have no doubt that javascript makes more use of logic that php.

We don't want a special case for 0. By your logic 12 == 'TEST' should be true. 
You are assuming a cast to boolean even though neither side of the comparison is 
a boolean. Note that true == 'TEST' will match because here we cast to boolean. 
But 'TEST' cast to an integer is going to give you 0.

OK, you are right. That was the explanation I wanted: it depends on the type you compare.
if( false == 'TEST') works correctly.
Now it makes a little more sense to me.
But javascript is still superior because inside a if() I suspect that any language should try to cast both to boolean.

A good rule to be implemented by PHP is:
If a comparison of simple equality ( == ) or simple inequality ( != ) is done between two different data types, PHP should cast both to boolean before comparing.

Because 'TEXT' casts to true, 0 casts to false so 0 != 'TEXT' makes more sense than 0 == 'TEXT'.

No it doesn't make more sense. This would make 12=='TEST'
You cast to a type in the comparison, not to some third type. Besides changing 
this would break millions of lines of code. Not going to happen.

12 == 'TEXT' in the "boolean" point of view is correct.
Javascript agrees with it.

So by your logic 12=='13'
Do you have any idea how much code that would break?
The web is not typed. Everything comes across as strings. And everyone does stuff 
like if($_GET['age']==19) { ... }
which you are proposing to break.
Same goes for data retrieved from databases. Everything comes back as strings.
So no, this is simply not going to happen. Please stop.

There is a solution.

See that all examples I gave were made using NON-NUMERIC texts. ('BOOK', 'TEXT', ETC) You are right thinking about numeric strings like '234'.

If text is numeric, php could continue treating them as numbers - that would be an exception to the rule.

BUT... if the text is NOT numeric (\D+) then it could be casted to boolean.
'12' '13' '1987' would NOT be casted to boolean.
'car' 'soap' '#ffcc00' would.

"If comparing a NON-NUMERIC text ex: "book" to a number, both will be casted to boolean before comparing".

That would solve the problem, I think.

Remember that
if(0) results false
if('BOOK') results true
so...  0 == 'BOOK' breaks the logic. Think about with calm. I will stop now.