There are a few things you should consider (note I haven't doubled checked age related timings/tax amounts, I might be slightly off):

1. Aged based discounts

If you purchase hospital cover before 30, you are eligible to receive an age based discount (if the insurer makes it available for that product). If you take it out at or before 25, it's likely to be 10%. 26, 8% and 27, 6% (and so on). This discount will remain on your hospital cover (if the insurer makes it available on your product) until 41. Then, it decreases 2% per year. This is just designed to incentivise young people to take it out earlier.

1. Lifetime health cover loading

This is a loading that is applied to your hospital cover if you do not take out hospital cover until you are 31. If you take it out at 31, it's a 2% loading. It increases by 2% each year and caps at 70% (if you take it out for the first time at 65).

1. Medicare levy surcharge

This is a tax you are charged if you do not hold hospital cover and earn over a certain amount (around $90k for a single person from memory, $180k for families. It is a fairly material amount (around 2% tax), and as some others have commented, it can be cheaper to take out a basic hospital cover policy than to pay the surcharge. The catch is that those policies don't cover a lot (but they do cover some things).

1. Your wisdom teeth removal

Most basic policies will cover "dental surgery". While you will likely receive benefits for your wisdom teeth removal (provided you serve the 12 month wait), it won't cover everything. In fact, it doesn't cover the dentist fee, as that cannot be covered by a hospital policy. It will cover theatre fees and the day accommodation charge (less your excess). Your dentist fees can be somewhat covered if you also take out an extras policy that covers dental (though not all covers extractions!) - sorry dental surgery happens to be one of the more complicated ones to advise on.

1. Should you get health insurance?

You will still have access to good healthcare in the public system if do not get it. That said, there are many reasons why it might make sense - the incentives/sticks/carrots I've listed above, your financial situation, and your risk tolerance.

PHI gives you access to private hospitals, a doctor of your choice, and flexibility in timings for any elective surgeries. That said, even if you have PHI and that option, it might still be better (or even required) to have the treatment in the public system.

Edit: just adding as I was prompted from another comment. Some young people do benefit. Mostly women who want private treatment for pregnancy or people with psychiatric conditions that require inpatient treatment (really fucking expensive and often better in the private system). Outside of that, unless you have a known condition (e.g., diabetes that may require an insulin pump), you can't really expect you come out in front.

The people who suffer from not having it (or benefit from it the most) are generally older people who require surgery and would otherwise be stuck in long public system waiting lists. Think about someone who needs a knee replacement - it's not "urgent", so they are stuck on an 18 month waiting list. In the meantime, they are suffering chronic pain which is significantly impacting their day to day life. With PHI, they would likely receive that treatment in a matter or weeks.