Time to first token is where input length shows up
Before generating anything the model must process your entire prompt. On a long prompt that prefill is often the largest component of time to first token, which means cutting input improves felt speed as well as cost.
Prompt caching helps here too: a cached prefix skips most of the prefill, which is one of its less-discussed benefits.
Perceived against actual
Streaming does not make generation faster. It changes what the user waits for — from the whole response to the first token — and that is frequently a five to ten times improvement in perceived latency for no engineering cost beyond handling the stream.
The reading-speed figure tells you whether streaming will feel instant: above about 250 words per minute the text arrives faster than most people read, so the wait disappears entirely.