There isn't much downside. 0% loans do exist, and when you get them they are glorious. The good ones are almost always a promotion to earn your business. New cars and credit cards are a perfect example. With rare exception, pay the minimums for as long as you can even if you have enough to pay them off in full. Take that money and park it in an interest bearing account or invest it if you wish.
As an almost funny aside, I'm currently 2 years into a 63 month 0% loan on a new car I purchased in 2018. When I bought the car I was trading in another (that I was also slow-paying due to a low 0.9% interest rate) and I had $5K in equity. The finance manager told me I was approved for the 0% rate, and asked me how much of the difference after my trade I wanted to finance. The car I was buying was $22K, and I said I'll finance the max he'll let me. He said he needed a number, so I said $50K. He kind of looked stunned and then smiled as he realized that I was trying to maximize the 0%. I said he can just buy my trade, then offered $500 down, so he cut me a check for $4500 and gave me my new car.
In the car sales example, the main downside of a 0% interest rate happens before the sale. A 0% finance rate has a measurable cost to the bank, which they may be willing to return to you if you don't take the special rate. Car manufacturers almost always offers 0% financing, or something else, typically in the form of cash back. The cheaper the car the more likely you should lean towards the cash instead of the low rate, but you can run the numbers both ways. In my case I think the cash offer was $1000, which compared to the alternative rate of 3.9% was not as attractive if I took the loan to full term. If I paid the loan off sooner the cash would have been better, but I preferred to utilize the money elsewhere. After the sale with your 0% loan in hand, slow pay it unless some contrived circumstances crop up where you wish to minimize your cash (divorce maybe?).
Another possible downside, though admittedly easy to mitigate, is that your debt to income ratio will be higher when you apply for future credit while the loan is active. But if you're choosing to purposely slow pay a 0% loan and you find yourself in a scenario where your DTI affects your ability to get a loan, you could simply pay off the 0% loan at any time to fix it. But even then, you'd probably be better off taking that extra cash and reducing the new would-be loan by the same amount instead, since presumably it would be at an infinitely higher interest rate than 0%.