Only make the sausage if they'll pay for it

It doesn't really matter how you make the sausage.
But the sausage had better be good and the customer
had better be willing to pay for it.  Regardless, don't start
making it until you are confident you'll get paid for it.

Sometimes it's really nice in projects to be given the opportunity of an "open" contract but it will frequently lead to disputes if you're not careful about managing customer expectations and the budget.  If you're not a professional project manager, you should not dabble with T&M contracts because you will get burned by hard-nosed customers that demand quality for their money (and they should).

It would be nice to bill people and see if they pay or not but you have to make sure when you're doing this that you're also able to defend your price and value for what you're billing.  This means that you have to have excellent metrics and measurements of the value you're delivering and a justification for that value (the business case and justification, ie the argument *for* the price).

Whether you're managing projects on a fixed basis (even Agile is fixed since it locks scope for an iteration) or on a T&M, more loosey-goosey basis, you have to be careful.  No matter how you're making the sausage, make sure that the customer gets it, is willing to pay, and likes you enough to fork the money over.  Otherwise, you might as well not start.