Well, in regards to breeding and shiny hunting: because it's not fun.
There. I said it. Relying on RNG to find or breed a Pokemon with the IVs and Nature you want - and Egg moves sometimes, too - is a time-consuming, tedious, and outright boring task. When the Pokemon obtained through using devices like Action Replay are possible to acquire in the games without them (i.e. they don't have stats, moves, or abilities that aren't programmed into the game) I personally do not see what the problem is. Some people do not have the time or the patience for competitive breeding. So they should be denied competitive battling because of it? This is fair...how, exactly? What if someone who works and doesn't have time for breeding Pokemon really wants to battle with their friends who do?
"Fun" means different things to different people. Some people just want to battle without the fuss and will take shortcuts, whilst others take pride in the Pokemon they spend hours breeding and training.
If anything, it benefits other people as well, because it gives them more opponents to battle. If someone is clearly cheating to give themselves an unfair advantage, then yes, it is absolutely wrong and you have every right to complain about it. But otherwise, no. You're probably not even going to know about it unless someone tells you. A shiny Pokemon with perfect IVs or whatever is perfectly possible to acquire without the use of a cheat device, so what difference does it really make to you?
It's not challenging, either. It's time-consuming. I really wish people could understand the difference between these two concepts. A challenge is a system of gameplay that does not draw upon RNG and other cheap mechanics beyond player control to frustrate your efforts to get what you want. A challenge is a system that you can fully manipulate (I am aware there are methods to manipulate circumstances in Pokemon games, so no need to point those out to me, thank you) to produce the desired results, but with significant effort.
There is no inherent difficulty or challenge in luck-based systems. Let's take a hypothetical scenario where two people are trying to find the same Pokemon with certain parameters; perfect IVs, a certain nature, whatever. They both use the same method. One person could find it on their first encounter. The other person could take 10 hours or more to find it. Explain to me the challenge in this...outside of needing an incredible amount of patience for something that ultimately might never reward you. With Pokemon, you don't always get back a reward proportionate to the time spent, because the odds are so ridiculously slim that you can literally never find what you're searching for.
Regarding event-only Legendaries: a lot of them are timed events. Almost all of them, in fact. You miss them, tough luck: you're reliant on either the goodwill of other people who use the GTS (which, let's face it, is in short supply) or even worse, you have to wait for Nintendo to release them again. Wi-Fi distribution is fantastic, but unfortunately these things aren't available permanently. So say you miss something...what, you're supposed to just go without? Why is it not OK to use a cheat device in that scenario to get one? Sure, these are things that aren't available in the game, but they should be. There is no reason that they couldn't be unlockable events through your actions in the game.
...and those that are. Some of them, like Gen IV's Arceus, Shaymin and Darkrai events, are locked behind coding barriers for no reason whatsoever. Arceus' event was never even made available in the West. Put this into context with literally any other series of video games...would it be acceptable then? Rather than asking what the point in using cheat devices to access these things is, I think the better question is: what is the point in even including these things if you're not even going to make them available through natural means? Why include it, but not include it?
Think of this whole thing more like drinking tea than having cake. Some people like milk and/or sugar, and others don't. Some people just have different tastes. It doesn't take the fun out of the game for some, and it doesn't take the fun out of YOUR game if other people cheat to acquire things, unless they are competetive battlers with Pokemon that clearly break the rules of the game by having abilities or moves that they shouldn't have.
Yeah, cheating really is not a bad thing. I wouldn't even call manipulation of a game's code to generate or access things that are naturally programmed into the game cheating at all, really. To me, cheating would be manipulating the game to generate an unfair advantage for yourself if you planned on interacting with others.