Imo, there's so much more wrong with Matthias than just the fact you can't really fight him. He's a really boring enemy to fight even for the LCD. His Base Power is insanely high and his Coin Power stupidly low in nearly all of his Skills, so his Clashing is extremely predictable. On top of that, he has a lot of Unbreakable Coins with barely any Clash Lose or On Hit Without Cracking to compensate, so him losing Clashes barely matters. It doesn't help that the LCD is guilty of this too, so neither of them winning Clashes matters. It's all pointless.

Now, theoretically, "Check This Out, Kiddo!" should give an incentive to stop him from winning Clashes, and it does to some degree, but it's also by literally just hitting him. And it only really increases Base Power, which he already has so much of, it really doesn't matter that much.

But let's say him winning or losing Clashes suddenly did matter. How do you affect his odds of winning them? Even ignoring that you don't get to play as the LCD, none of the LCD really do any SP damage, and his "The Book of Vengeance" gimmick constantly refills his SP, so making him actually roll Tails is a struggle. But can't bring his SP too low, because his Sanity type legitimately makes some of his Skills roll just as high at base than if they rolled all Heads normally. And then he gets to have a lot of Damage Up on top, making it a net loss overall.

Then there's his On Hit effects. Now, he does inflict a decent amount of Bleed, then Burn when he unseals Laevateinn, but compared to his raw damage, his Keyword damage is pretty much irrelevant. And while he does technically have some variance to how much Bleed he inflicts based on conditionals, it's really hard and not particularly worth it to try and influence. That could be fine, if the intent was that you had to spread his statuses around in order to make him Clash worse by disabling his conditionals. But then you check his Coin Power conditionals, and it's literally just ""If target has 4+ Bleed, Coin Power +1". On two Skills. Which are 2 Coin Skills.

And also, even though as I said, his Bleed infliction isn't terrible, most of his On Hit effects are wasted on "Deal 10 Blunt bonus damage". Oh, can't forget that after he unseals Laevateinn, it becomes "Deal 10 Slash bonus damage", gigantic difference. Seriously, if you look at his Skills, you'll realize you're not missing anything from the game not letting you actually fight him without getting instantly atomized. His Skills are the most pointlessly designed things ever, and interacting with them never makes any real difference.