Koopagenics (Part 1)

That's why jack black played bowser. He's The Dragon Warrior!

God bless the algorithm for bestowing this gift upon me

The answer is they don't actually make more of themselves in that way. Canonically in the Mario world all characters from Kongs, Toads, Humans, and yes Koopas are delivered by Storks from a magical place. So yes it is magic based, and given the way it's described it's probably Wish/Star magic based. The only exceptions to this is Yoshi whose entire species can lay eggs which become more Yoshis, and any plants like Piranha Plants. Magikoopas creating life from blocks using their magic is probably connected to the same magic as stated before. I have a hypothesis that the black magic of the Koopas is stolen Star Magic that is limited by 3 symbols. Koopas are various species, there is no one species of Koopas. The Koopa Troopas for example, I call them the Common Koopa since not all Koopas of this species are Koopa Troopas. But at their core they are alll Koopas, their own grouping of turtles in this Turtle Tribe. I'd note Spiked Koopa's abilities could be tied into the shell he chooses to wear. We know shells are more of clothing, gear, or accessories that can have different affects on who wears it and even serve as a type of a power up. Yoshi's while it's been suggested by Tezuka that was supposed Yoshi is a type of Koopa, and he even claimed Yoshi is a Koopa. The manuals and in-game lore says otherwise. Yoshis are referred to as dragons or dinosaurs which seem to be interchangeable in the Mario World. Yoshi's are constantly referred to as dinosaurs or dino-dragons, and referred to as prehistoric. Yoshi's come from Dinosaur Land in addition to all of this. While the saddle on Yoshi's back is a shell, this doesn't mean Yoshis are turtles because of it. As stated before shells work as gear and clothing and can be worn by others who aren't Koopas. Such as Konkadors, Ant Troopers, Goombas, and even Mario and friends. The Yoshi that you should from Super Mario World and compared to the 3d model of Yoshi, and suggested their are different species more suited for riding. The problem there is that is the same Yoshi, not 2 different ones. I have to point out the ability to breath fire and be reptilian doesn't make one a dragon. Outside of Mario not all dragons breath fire, some spit water, some have poisonous breath, a poisonous bite, or no of that. In addition breathing fire doesn't make you a dragon either. Case in point, Fire Chomps. Bowser didn't intentionally turn into Fury Bowser. He was turned into that by accident by Bowser Jr. who used his Magic Paintbrush on him as prank.

What's interesting yo me is how you mentioned Bowser's strength and power being important to him. In fact, it's... Kind of strange, right? Aside from the very occasional other threat, Bowser is usually the de facto problem causer of Mushroom Kingdom and/or the world as a whole depending on the game and setting. What in the world is he trying to protect the koopas, his kingdom, from? Is the constant kidnappings of Peach and assorted assholery just a way to keep his warfaring people busy, and inspire confidence in them as to his capability as a leader?... I'm not even sure it's necessary. We talk to plenty of koopas, and aside from cowardice or the introduction of magic, they're all uncompromisingly loyal. To a fault really. It's just strange... What's his aim in being the baddest bad guy in the mushroom kingdom? Is it really just a midlife crisis, or is there more to it?