Yes, there are some things that can be done here. But first, it's important to position AI properly. AI is not the product, its just a tool, and the product is personalzied medicine.
The acquisition of training data can come from 2 parts of the world of patient data. First, deidentified patient EMR is of some perhaps very high value. You can attempt to collect this or you can buy data sets. For example, I believe United Healthcare (among other groups) will sell you a large database of deidentified EMR records for a couple hundreed $K.
Then there is genomic data. You can go buy it for a lot of money from HLI if you want. Or you can offer a sequencing service and subsidize the cost in trade for contributing the use of the data back. Regardless, this is a big undertaking. But there are more human sequence databsaes being put into the public domain for research that coulde be used.
Then there is the issue of getting the right data and cleaning it. You have to know what question you are answering first. This is expensive and if you get the wrong data, it is a waste of time. AI is only as good as the data underlying it (assuming youa re tal;king about machine learning).
How can you extract value from the AI? Well again, the product is not AI, it is personalized medicine. There are 3 communities that might pay. Consumers might pay but are usually reticent to pay for an app, But their employers or payers might pay for them to have a PM app provided there is a reduction in the cost of healthcare ebnefit. That has to be proven.
What about providers? My belief is that providers will sue a PM app if it is validated and it doesn't cost them. Providers don't like to pay. Maybe they can get a payer code for a use, but i am not aware this is done yet.
Regardless of who pays (consumers, employers, payers, providers, or even governments), a true PM app or system will have to link the communities together (paitent, provider, payer, pharmacist) for communicaiton purposes and enable the aptient to share recommendations.
AI may underly the decision making, but what they buyer would pay for is not AI, it is personalized information and recommendations.

I start with a definition: Personalized medicine is a form of medicine that uses information about a person’s genes, proteins, and environment to prevent, diagnose, and treat disease. In cancer, personalized medicine uses specific information about a person’s tumor to help diagnose, plan treatment, find out how well treatment is working, or make a prognosis.
Is the current state of medical knowledge and technology able to do this? Only in a very small part; and it is not a question of money - "medical art" is still not at the right level.
How should a healthcare system pay for this? Diagnosis of disease would need to be given a code, with appropriate sub-codes for activities such as gene analysis, protein analysis, etc., with all this being validated to confirm that such activities indeed arrive at valid diagnosis.
These tasks are currently not within medicine capabilities to accomplish.
Further, provided all the above can be done for a patient, the task remains of selecting what available medication should be used. Existing medicines are approved to be used for a defined group of patients. As it is now, the best one can do is to match individual patients to the most optimal drug. True personalized medicine would require that medicines are developed for individual patients, however, this would certainly be cost-prohibitive, with or without "artificial intelligence".
A side comment: AI - artificial intelligence is indeed "artificial" since information needs to be provided for the so called AI to sort through it. Until such time that algorythms are developed for actual thinking processes by machines to be possible (such as for example in the game of chess), the approach is not really an "intelligent" one. (intelligence, noun: the ability to acquire and apply knowledge and skills. Currently, the knowledge and skills need to be provided...)

Setting aside clinical data streams for the individual, fed from a variety of sources, such as for example an IoT-based clinical monitoring data collection arguably streamlined moving forward via layers such as the seminal EdgeX framework, a best approach to de-identified training datasets might be industry-based or government-driven via EMR or mandatory reporting for providers rather than from single organisations. Higher level might arguably mean better data, albeit segmentation (context, demographics, standards of living and other environmental factors) is of course critical to avoid skewing and biases.
The questions of value and monetisation depend on local regulative conditions and how is health considered within such polities, in addition to other socio-economic factors: the economic models are widely different from a country to another (private, public, hybrid), at times from a state to another and what works in a particular area might be irrelevant in another.
For example, in eldercare, the residential approach in many Western countries would unlikely work well in other regions where social fabrics articulate around multi-generational dwellings. This situation in turn would result in quite distinct economic models for PM. In the case of US, Ed’s answer is framing well the way to approach this: the product is PM rather than AI.

The question starts by stating: " I am a firm believer of the power of AI." The current capabilities of AI appears to be limited to successfully understanding human speech, competing at a high level in strategic games such as chess and Go, operating autonomous cars, intelligent routing in content-delivery networks, military simulations, and interpreting complex data, including images and videos.
It is the last item the question likely refers to. Relevant complex database useful for PM will take some time to generate, and will cost a lot of money. Contemplating profits at this stage would seem irrelevant. Further, "PM" in this context could mean "personalized medicine" but I would say that it is "precision medicine" that is needed. What is the difference? It is very unlikely that personalized medicine, i. e., medicine developed for each individual, is a realistic proposition. On the other hand, medications are needed that act specifically on a correctly defined disease targets, treat or even cure a disease without unacceptable side effect, that would be validated to have a therapeutic effect on patients accuratelly diagnosed to be inflicted with the disease in question and the same target on which the drug acts - i. e., precision medicine. AI could be employed on the way to this goal, but by itself, AI will not do it!

personalized medicine to the extreme might want to be so personalized that the uniqueness of the situation is not repeated before which we can call "unKnown". So there will be not enough sample data to feed machine learning methods to get the rhythm or reason to creating a treatment of confidence. This is a paradox which is not strong with current learning based AI which need to follow "Known-> Known ".