Except if your mind worked like that, you'd never be creative. To think you can focus on one thing is to ignore all the times you came up with a solution to a problem after ignoring it for a while and doing something else.
And in any case, nobody says you have to focus all the time. But if you make no room for serendipity, serendipity will not occur.
It can't if you actually focused 100% on washing dishes. Which is my point exactly, which you seem to be perfectly missing.
The whole concept of 'mindfulness' is contrary to serendipity. It is also, thankfully, contrary to how intelligent minds work.