frenchyd,
I've read the entire thread. I respect you and what you're trying to do. I've put some thought into your question.
To re-state, your 16-year-old granddaughter has many accomplishments and has the potential for more and even greater accomplishments. Her family doesn't have a lot of money and you want to help her achieve her potential. I think this is a good thing and I applaud you for it.
1. What is her skill level as a driver? I've sat with hundreds and hundreds of teen drivers and at least half of them haven't yet developed a basic level of competence or confidence. So many teens wreck their first car. Some people (teens and adults) never develop proficiency as a driver. It's up to you to decide if she has the competence and confidence for a new car.
2. You're thinking long-term, 10-15 years, and things can change fast for a 16-year-old. How long has she wanted to be a doctor? If her anticipated commute is 5-7 miles for her undergrad and she's close to home, I think she can get by with something less than a new car. If med school takes her far away, solve that problem in four years when the car market is hopefully less out-of-balance.
3. This is only my own personal parenting belief, and my kids are still young, but I feel that a new car at 16 years old can set an expectation of standard-of-living / lifestyle that makes it more difficult to be appreciative and content in the future. I bet many of us GRM folks would attest that starting with "rougher" cars when young helps us to appreciate nicer cars (and nicer other things) later in life, and to be more content with less material things.
4. Training for the Olympics is probably mutually exclusive to going to medical school. Maybe she can delay med school until after her hockey career but has she thought through how to navigate both? If med school is delayed that might change your decision on the vehicle.
5. I would focus on what she needs, which for the next four years is likely to be transportation over a short distance, often in inclement weather, but not far from home. She doesn't need extra expenses for gas, insurance, maintenance and repairs, or headaches due to unreliable transportation, and she definitely doesn't need extra pressure to make more money or to make loan payments. She has an arrangement with you for $300 a month.
6. My suggestion is you make her an offer where you provide her transportation in exchange for her cleaning your house twice a month. In this scenario, you choose and own the car yourself, pay or finance it however is best for you, you retain title, you cover all the expenses including insurance and maintenance, and gas, too, if you want. She gets transportation as long as she cleans. This gives you both lots of flexibility. If her needs change, if housecleaning doesn't work out any more, she can move on and you still own the vehicle. If you want to change your stable of cars you can, just continue to have a vehicle available for her. She could continue to drive your truck until gas costs make it advantageous to put her in something more fuel-efficient or electric. After her undergraduate schooling if she goes away to medical school you can gift her the car, or keep the car and simply waive the cleaning requirement, whatever you think is best at that time, or if she doesn't need a car in med school then the car reverts back to you. She gets the transportation she needs in the near future without being locked in on a loan, without being committed to a particular vehicle for the 10-15 years it takes to make a new vehicle financially advantageous, and she avoids the stress and headache associated with the expenses and maintenance risk. You get to decide whether new or used, gas or electric, car or SUV, makes the most sense.
Just my thoughts and they're worth what you paid for them.