That doesn't really appear to be the case as GPT and Anthropic models appear evenly matched despite Anthropic encoding the same text into almost ~2x the tokens...
I'd also - naively - assume this would make training their models more expensive. Though inference now dominates, and they'd probably rather have more tokens than less (to charge you for them at future 80% margins).
the Anthropic tokenizer is not worse, its more expensive/verbose