I'd dispute it's American humour, it's very much a trope established by British comedy such as Monty Python and carried on through programmes such as The Fast Show.
The humour is in the repetition and the recognition that the punchline is coming is what appeals to some, it creates a feeling of being "in in the joke".
Some American shows such as Family Guy have used this to great effect, though arguably the reliance on the repetition of punchlines has over time become the reason it has been deemed to have dropped in quality.
As to whether Haymaker's excited response is humorous or humourless, that's up to the individual. Personally, I'm a fan.
All true, but for repetition to be funny, it needs to be well timed, and repeated sparingly.
Most sketch show have repeated gags, but only ever once per show.
Think of Victor and Jack saying "2 pints prick" or Catherine Tate's Nan saying "What a f***ing liberty" etc etc.
We're all waiting on the line, but we only got it once a week.
Haymaker's gag is fine, but it would be funnier if it was used more sparingly, imo
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