The problem is we must start from scratch based on being a territorial people once again.I'm certainly not persuaded that efforts to rebuild the Temple would strengthen Israel's political hand. And as I've said many times before, there should be no digging on the Temple mount apart from scientifically-controlled archaeological excavations, preferably at a (probably not too distant) future time when they can done nonintrusively via molecular technology and the like.
We need a new approach to religion if, for instance, we are to combat the J Streets, Goldstones or George Soroses of this world, not to mention appealing to the imagination of questioning disaffected youth; and the first step should have been to start rebuilding the Temple.
This does not mean one should revive the priesthood or the sacrificial cult. You need living symbols to move the people. If nothing else, Herod showed us this and the durability of the wall he built is its final proof.
Unfortunately, Rabbinic Judaism can no longer provide us these. Two millennia, yes, and up to the Holocaust. But no further. It cannot provide us with the blueprint for becoming territorial once again. Moshe Dayan was wrong in ordering the Israeli flag taken down, in effect, surrendering sovereignty and giving the Muslim Wakf control over the Temple Mount. No self-respecting people after two victorious wars would have behaved in this way. But he had no guideposts to rely upon, only egocentrism and his own pragmatism - plus he loved the grande geste.
But now, almost three generations after the Holocaust and with its memory beginning to fade, we have nothing positive to appeal to our young generations in Israel and abroad. It is poetry and the spirit that provide this. They are the positives, not humiliating renunciations. The reconstruction of a Temple - any Temple - should have begun 40 years ago and we would be well on our way toward achieving these things. This does not mean we should emulate the old design. Its content, shape and operation should be open to investigation, even architectural competitions, and creativity; but the symbol would be there.
It took the Herodian Temple almost 90 years to be completed. Ours and even its early stage - archeological investigation - hasn't even begun. People need a positive historical Judaism to go forward and this does not mean a Roman/Herodian-sponsored Phariseeism. People need positive symbols to rally around. The time is late. There is plenty of room on the Mount for everyone.
In no other manner can we gain the respect of the world and regain our own self-respect, and the world come to understand us - and we come to understand ourselves.
For Herod's Arab background, see here. For the recent discovery (perhaps) of Herod's tomb at Herodium, see here and here. I don't see that Herod's background and character are going to have much effect on the symbolism of the Temple for Judaism.