I had a difficulty comprehending the utter ridiculous reason, that Ollivander gave, when I asked him, why he didn't use other cores.
"Those are the strongest magical creatures known to the world."
I nodded and nodded, and blanked out, as I kept thinking of Thunderbirds, Nundu, Basilisks, Graphorns, Zouwu and even Thestrals.
Granted, they weren't known as the most strongest or usable for general wizards due to rare sightings of Thunderbird, and their temperamental nature; extreme fatality to Nundus, which made acquiring their hair, whiskers or heartstring, incredibly difficult; and Thestral wands were apparently accepted if someone could face death willingly; and there were no sightings of Basilisks until recently, and the only known wand made from Basilisk, was Salazar Slytherin's wand according to wandlore. Just like Thestral hair was used in Elder Wand, and apparently only used by Antioch Peverell.
And this modern wands followed the same principle, which the muggle world understood a century, ago. It is cheaper and easier to make products with limited variation in large volumes, than it is to make customised, personalised and cheaper items with same quality and with fewer mistakes.
This was why, mass produced items became the norm, and factories and industries came into place. The Industrial Revolution was centralised around the idea to generalise everyday to produce staple items, with limited variation, and charge less for it, while making customised items and products for an expensive price. That is why handlooms and handcrafted items lost their way to cheaper mass produced items which common people could afford.
And all that is understandable, when the British wizards and witches, before Garrick Ollivander took over the shop from his father, would bring mediocre cores like Kelpie hair, Kneazle whiskers, Billywig sting, Dittany stalk and Mandrake root, which had personal significance to Garrick's father and expect a superior wand, from inferior cores.
That was the source of struggle for him, and when his son saw that, he became the Henry Ford of magical world, and began to offer the three superior magical animals as cores for the wand. They were reliable, strong and powerful, capable and most acceptable to regular masses who could neither afford a customised wand, nor need one in their entire life.
In my case, my magical reserves, and changes after the ritual meant that other wands would not accept me. Dragon Heartstring might, but it seems, even a wand made of Hebridean Black Dragon's Heartstring refused to be paired with me.