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If you fix a price with the taxi to take you to the local airport and half way there you decide to go to Heathrow instead, can you reasonably expect the same price?

No - and surely the key to this will be defining the work you're going to do for the agreed fee? If the client changes their mind, then that's a basis for a further discussion. Same with complex litigation - you phase the work and agree a fee for each phase as you go along and carefully define the work included each time. It's entirely doable - but not easy; if it were - I suppose everyone would be offering it and it wouldn't be a differentiator for QS!