The thing is, it's not just an overload; it's an overload
and a typecast. Those are two separate questions, and OP is really complaining about the typecast, not the overload.
The ints vs. floats thing is kind of a red herring. In that specific case, at least you're still talking about numbers. The argument against having contagion for 5 + 5.5, and overloading for "5" + "5.5", but throwing an exception for "5" + 5.5 is that the first is a pair of numeric types, the second is a pair of strings, but the third is a pair of unrelated types. You can say white is lighter than black, and a feather is lighter than an anvil, but you can't say that white is lighter than an anvil because that's nonsense.
Incidentally, this is why, say, Python and Ruby (and I imagine Lisp) people insist upon the distinction between dynamically typed and weakly typed. If I fire up a node.js repl, I find that '50' + 5 is '505', but '50' - 5 is 45, and am reminded why JavaScript drives me nuts. In the extreme you get things like [this](http://phpmanualmasterpieces.tumblr.com/post/33198366857/lay...) and [this](https://www.destroyallsoftware.com/talks/wat). I realize that Java probably doesn't do anything near that bad, but the point is that it's a question of balancing convenience vs. error prevention, and that we're talking about a very strictly-typed language which will naturally attract people who tilt toward wanting the error detection, and even dynamic languages that swing the other way on most things often find that you don't need to make your math operators cast numbers into non-numeric types (and risk the resulting runtime errors) to have convenient string handling.
In fact, I think Ruby's string interpolation is actually a better syntatic sugar than Java's `+` cat overload. Consider that I want to print a string along the lines of "1 + 5 = 6" but with arbitrary integers. Here's how it might look in Ruby:
puts "#{x} + #{y} = #{x+y}"
It's hard to imagine a syntax much better than this, especially for short strings, since the shape is basically identical to the string it's creating.
Python 3 is less pretty, but still reasonable:
print("{} + {} = {}".format(x, y, x+y))
print(x, "+", y, "=", x+y)
Meanwhile, neither Ruby nor Python makes you declare types as a rule. In fact, one of the non-backward compatible changes in Python 3 was to make it so that 1/2 returns .5, since that's how numbers work and it's probably what you meant (there are still ways to specify integer division if you want). However, in either language, if you write "5" + 5, they will raise a ValueError because that doesn't actually mean anything, is likely to be a bug, and is always easily rewritten in a concise but less ambiguous way. Speaking of which:
> have no potential to mean something else than what the programmer meant
is just false. There is a very obvious way for it to mean something other than what the programmer wanted: When the programmer forgot to cast a string to a number and tried to add it to a number. This is particularly a risk in dynamic languages or those using type inference (it's harder to pull off in languages where you have to explicitly declare all your variable types, which may make it a non-issue in Java speficially).