It's a common misconception that the sale price of your home makes your taxes go up in Michigan. In fact, it's a misconception that your taxes are guaranteed to go up at all. Here's the most straight forward answer I can give on why taxes usually go up when you buy a home:
SEV vs Taxable Value
The county you live in has two numbers attached to your house called the "State Equalized Value" (SEV), and the "Taxable Value".
For the sake of keeping things simple, the SEV is the market value of your home.
The Taxable Value is the number used to calculate your property taxes.
When you buy a home, your SEV and Taxable Value are the same number. Michigan has a law that says property taxes can only go up a maximum of 5% every year for people who already own a home. This means that even if your SEV goes up 10%, your Taxable Value can only go up 5%. If this happens over a few years, there ends up being a big difference between the SEV and Taxable Value.
Once a new buyer buys the home, the Taxable Value is reassessed for the new owner at whatever the SEV is. So now, the SEV and Taxable Value match again, and the process starts over.
I buy a house with an SEV of $100,000. Because I'm a new owner, my Taxable Value is now $100,000.
I live in this home for 5 years and home values go way up in that time. After 5 years, my SEV is $146,932. Luckily, because of the Michigan law I mentioned, my taxes were only allowed to go up 5% every year, so my Taxable Value is only $127,628.
After those 5 years, I decide to sell my home. The new buyers are going to have their property taxes reassessed by the county. This means the Taxable Value is going to reset up to the SEV amount, which is $146,932. This is why their taxes go up. The sale price of the home was irrelevant.