You do realise that Andy Hug lost to Ernesto Hoost thrice, and Peter Aerts twice. And I know you will call them kickboxers, but most people know them as thai boxers.
The reason a karateka is the K1 champ is because under K1 rules, and K1 rules will not allow elbows to the head, no clinching/elbowing, or clinching/kneeing. If you do one, you can't do the other. Taking away some of the benefits limits the effectiveness of muay thai.
If you search youtube, you will find a fight between Changpuek Kiatsongrit versus Hug in kyoshukin rules. The first round, the lighter Kiatsongrit was killing Hug. He wanted to clinch, but was chastised by the ref. This is the same fighter who made Rick Roufus, and brother Duke become Thai fighters after he destroyed Rick in a kickboxing match.
You talk about Lyoto supplementing his karate with muay thai, why don't muay thai fighters supplement with karate? Anderson Silva got his black belt in TKD before starting muay thai, is he considered a TKD stylist. GSP, Bas, got started in kyoshukin, but all of them gravitated toward muay thai. WHY? I don't think GSP is training karate when he trains with his primary stand up coach Phil Nurse. Duke Roufus was an American kickboxer who now teaches Muay Thai under Master Toddy. Why? Xtreme Couture and all the camps listed above have Thai trainers, but no Karate, WHY?
Again, Karate does have it's merits, but please, if you will, address these questions. Anderson Silva's, Alan Belcher's Muay Thai looked pretty good tonight, didn't it?
I already answered all this in my long post. Shit, I'm going to start quoting myself.
There would be no point in Bas continuing to train karate because he's already and expert, and the additional moves they teach in karate aren't ring-legal. He already learned how to do a front kick and a roundhouse kick expertly in karate
before he ever started Muay-Thai.
How many katas and bareknuckle matches has he already been through in knockdown karate? Thousands.
It would be a waste of time to continue practicing this
He's been there done that, and he'll still use it in a street fight. He's an expert in karate.
Muay-Thai means more time he can train for the ring-legal strikes. In a recent interview he said he still does katas though.
The rest of your post is speculation. True Muay-Thai guys train more in the clinch, but they don't have Andy's signature axe kick, spinning back kicks, side kicks, etc. All those kicks take real training to use effectively,
so you won't so it from the sloppy hayseeds Dana promotes on the UFC, cept from GSP.
In fact, I rarely see a decend front or roundhouse kick from UFC fighters, save GSP and thats from training in Karate 10 + years.
Clinching is grappling. All things being equal, size and strength, I believe the very best karate guy will beat the very best Muay-Thai guy. Like I said though, Karate has all the techniques of Muay-Thai and more, thus it takes longer to become good at it. What opponent are Muay Thai guys facing when they punch a bag? Is that a resisting opponent?
This thread is called Muay-Thai vs. Karate...
Well guess what, Muay-Thai vs. Karate already happened in 1963 and the Karate guys won 2 - 1 in Lumpinee stadium, Thailand
long before people started crosstraining I might add.