There must be some misunderstanding here... If the amortization schedule on 100k loan at 3% amounts to about 52k in interest over 30 years... if I pay the loan in 3 years I doubt very much that I had to pay them the 100k principal+52k in interest.
First of all, there are other mortgages available, they are just rarely used. 99% of all non-commercial mortgages lock an interest in for a certain amount of years. The longer the rate is fixed, the higher the interest rate. Most people lock them in for ten, we did for 17 years, which was the full mortgage.
In addition many mortgages have a clause that allows you to make an extra payment once a year up to a predefined amount. With our current mortgage this is 5,000 Euros in a single payment once per year, with the previous one there was none at all.
You sign a contract where you agree to pay a fixed interest rate and the bank guarantees you that no matter what the market condition is that you interest rate doesn't change. You don't benefit from falling interest rates, you don't suffer from raising interest rates. As this is a contract, you can't just decide to quit. If you want to terminate early, you have to compensate the bank for their losses. Same thing as terminating a mobile contract early in the US.
What you owe is the interest the bank would have received minus any expenses the bank would have had if you continued with the mortgage, so management fees, insurance, etc. This is limited to a maximum of 10.5 years, because after that you have a legal right here to terminate a contract. After ten years, you can never owe the bank more than 6 months worth of interest.
For a thirty year loan of 100,000€ at 3% that you want to pay off early after three years, you probably have to pay about 15K in prepayment penalties.