Hi! You took the time to write out quite a detailed post, but I noticed a significant number of errors and faulty recommendations. I just thought I'd take a few steps toward setting the record straight.
1.e4 e5 2.Qh5 Nf6, your second diagram. Actually I think 2...Nf6! is Black's strongest reply to the Parham. It's true that White can capture the e5-pawn with check, but Black replies 3...Be7 followed by castling. White ends up way behind in development, and Black even has opportunities to rip open the center and attack early, or to trap White's queen if he is not careful, e.g.
Your point about 1.e4 e5 2.Qh5 Bc5 was quite valid. Black however doesn't have to lose a Rook after 3.Qxe5+ Be7 4.Qxg7 Bf6.
Your comment that there is only one solid defense to the Parham is the most blatantly incorrect thing you said. Here are many:
If you are an amature player, like myself, you will eventually and frequently encounter the Parham Attack, or as I not so affectionately refer to it... the Patzer Opening.
The Patzer is:
9/10 times bc4 comes on move 3 regardless of your response.
Now if you are trying to learn the game of chess, you may know that principles of a solid opening include Playing for the center, and not bringing the Queen out to early.
This opening brings the Queen out on move 2, and to a side file. So you know it's bad, but let's just say that you fall to it anyway.
There are 2 BIG reasons that this thing works at our level:
1. You try to take advantage of it and move with tempo for example:
However, if you did this you know the result is pretty nasty. opponent responds:
Lost your center, and in check... now bad things happen very quickly. you also may have tried using the pawn to knock the queen back:
Which yields:
and again a lot of bad things start to happen very quickly.
So you decide to do some research and the advice your often met with is "don't try to punish the early queen right away, just develop attacking her at your leisure to gain tempo. Wich leads us to the second reason this thing works:
2. You can not adhere to all the opening principles and successfully defend the Parham Attack.
For example maybe something like:
Great now he checks you and can collect your bishop:
Blocking with the your Queen saves the Bishop, but then this happens:
So in short it works because we are learning to play solid chess, and this attack violates everything we are taught. Further more it is worth noting that this attack may even actually be solid. It sees GM play sometimes, and has yet to be refuted the way something like "Damiano's Defense" has been refuted.
The Good news is that solid or not, there is only one solid defense for it, and it's very short, no lines.
You play:
The Knight defends your pawn and prevents the check. Your Queen stops the opponents Bishop and Queen duel attack, and from here you can go back to solid play.
He voilates the early queen principle. Your defense has to meet him, and thus requires you to also break that principle.
From here on out you have a much easier time developing than he does.
I have not lost to this opening since I started playing that defense. Even if the Patzer is a valid opening, noone at the amature level plays solidly enough to use it right. So there you have it.