I think we can safely say that the price of buying the Israelites' freedom was the devastation of Egypt's land, and above all the killing of Egypt's firstborn. The redemption of the firstborn of Israel was to remind them of the high cost of their liberty. Those Egyptians, brethren, belonged to God just as surely as the Israelites, but God used them to pay for Israel's liberty! They died so Israel could be free, and that law was established to remind them that people had to die so they could be free. Freedom is not free. It is the most costly thing in the universe, and once that freedom is gained it is not to be given up on the cost of anything. It is too precious to relax and allow it to just go floating by the board, especially when we begin to realize that for our freedom the greatest price in all the universe had to be paid.
This is having to do with the redeeming of the firstborn. And if you did not redeem it, you broke its neck. Of course, all firstborn Israelites had to be redeemed, but the animals, if they could not redeem them, had their necks broken.
It was this dedication, and redemption of the firstborn that was the sign. Not the little scrolls in the boxes with the leather straps.