There are big advantages to alphabetic texts.

The three advantages that you cite are not.

1) there is no less fighting with syntax when you use a graphical syntax than when you use a textual syntax. Now we can agree that a lot of textual programming languages have horrible syntax. I would advise you to try Common Lisp or Scheme. The use of S-exps (Symbolic Expressions) in those languages is a recognition that the syntax doesn't matter, and therefore the uniform and systematic use of the forms: (operator argument argument) for all the language elements is a big simplification at the lexical level. However, there still remain a syntactic element, an essential one, where you have to know that eg. the IF operator takes three arguments, a test, and then-expression and an else-expression, in that order:

(IF (= 1 a)
(print (quote one))
(return (quote done)))

By the way, notice how the addition of formatting (inserting newlines in strategical places) and indenting, makes a textual form look like a graphical one. This helps reading the text.

2) It is not easier for beginners to pick up. Only to children who don't know how to read yet. But then, one may argue that they ought to learn reading and writing before trying to write programs. In anycase, at this age, you would rather use objects than graphics, to let children play, programming "robots" by putting operation blocs into slots in a specific order.

3) Ok, it's your opinion, but graphical forms do not make it easier to find logic errors. They may help in getting an impression, and forming a mental image. But it would be dangerous to rely on them in a rigorous reflection about the program properties, just like it is bad to use the graphical diagrams to reason in Euclidian geometry. As goes the saying, geometry is the art of making correct reasoning using wrong graphics. Actually, you can do all geoemetry purely in textual and logical form, without ever using graphics, because the geometrical objects are abstract objects, and the graphical forms are only coarse approximations of the geometrical concepts. Similarly, the graphical forms of algorithms and programs, are but coarse approximations of the program logic, which is better described using text.

There's also another inconvenient of the graphical forms: they lack abstraction. You can zoom in and zoom out, and sometimes, you can even hide subcomponents in closed boxes, into which you can navigate graphically to discover the inside diagram, but by definition an abstraction is naming a concept. And text is better for names, if only because of the combinatorials. Take a standard human, and try to determine how many gestures, or how many different ideograms he is able to create and later recognize to identify different concepts. Similarly, count the number of words or names he is able to create and use to identify those concepts.

Finally, there's the question of the complexity of the tools required to manipulate graphics (and animations at that, if you want to manipulate sophisticated graphic views), vs. the tools required to deal with text, with a clear advantage for the later.

And let's not forget, at the beginning was the Verb, not the Image, and it's the Verb who was Creator.

That said, graphical forms can still be useful in the context of programming, notably when you want to explain some concepts. You can use various kind of diagrams, to present facets of software (cf. eg. UML), and other free-form diagrams. But either you have some formalized graphical syntax like UML, and therefore you bring the complexity of reading and writing correct meaningful diagrams, or you are left with ambiguity usually found with graphical forms, and you can only use as an illustration to some textual description.

You could also compare a program drawn in Piet vs. the same written in any textual programming languages :-)
Can you tell what this program does: http://www.dangermouse.net/esoteric/piet/Piet_hello_big.png
http://www.dangermouse.net/esoteric/piet.html
And what about this one: http://rosettacode.org/wiki/Hello_world/Text#Modula-2

That said, if you read Asimov's Foundation serie, you may remember the room where the psychohistorian mathematicians worked, where mathematical formulae were displayed on all the walls of the room and where they could explore and manipulate them graphically with gestures and other input. I'd agree that it is possible that eventually we have sufficiently smart AI programs to be able to write programs and other mathematical proofs in graphical or such dynamical modifiable forms with simple and easy input (ie. with the system basically guessing what transformation or addition you mean from your grunting and waving). But I don't see that practical before AI is achieved.