It's complicated because the costs are borne by a number of different parties: the patient herself, her family, the insurer (private or government).
For example, a patient could live longer but develop disabilities that require extreme measures in terms of treatment and family care, and cost a lot of money. The risks of all these are going to be unknown in very novel approaches, and people with different values are going to vary in their preference.
Understanding those risks and developing guidelines on when to pay for what are one activity of the FDA and major payors like Medicare. A patient and family facing a decision about the value to them in a time of crisis is going to be a lot less informed than those agencies, and it will be a lot easier for a doctor to mislead them (intentionally or not, but doctors aren't immune from over-optimism that their clever ideas might work).
At the same time, it does seem like there should be some protocol where a terminally-ill person can be considered sufficiently informed to take the risk. This is hard, because the risks accrue to individual parties (e.g. the university getting sued in this article) whereas the benefits are diffuse (medicine learns whether induced brain infections improve survival in glioblastoma patients). But without this protocol, we are always going to have stories of patients whose treatments and deaths could be teaching us life-saving lessons if only we could legally do what they want to do.
If the patient's best interests are no longer the primary concern all kinds of shady things become possible.
People can seek pain relief, mental health services, etc. that they might not be able to pursue if they take a risky procedure.