Whole genome sequencing and single cell sequencing are actually surprisingly inexpensive (compared to the cost of almost any cancer treatment) and there is a good argument that we should do this by default for any type of cancer for which there are not effective treatments.
I would encourage all patients to learn as much as possible about their own diagnosis. There may be clinical trials available in another centre that your clinician is not aware of or tumour-agnostic trials that target specific mutations that are present in a range of different cancers.
There is a good argument for allowing patients to try experimental treatments once standard treatments are exhausted. The provider liability issues could easily be solved by legislation. A bigger issue is that there will always be people who want to exploit vulnerable cancer patients by charging exorbitant amounts for plausible-sounding treatments which have no evidence base.
As an individual trying multiple experimental treatments at once is the logical approach if there is no other option. However it will not be possible to know which of these is effective and which have caused side effects so to develop more effective treatments we do need structured and carefully controlled clinical trials. Unfortunately there is a huge regulatory burden for any kind of clinical trial at present and this should be massively streamlined for cancer patients where even if the treatments cause harm the alternative is death.