Pay cash for primary home or put 20% down

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I have decided to downsize from the house I currently live in which is worth $600k, to a house that is worth $350k. After selling my current house, I expect to receive enough in proceeds from the sale to pay for the new house in cash.

I’m trying to decide if I should buy the new place with cash and be totally debt free so I can commit most of my future income to purchasing rental properties, or I could put a 20% down payment on the new house on a 30 year mortgage and then have enough remaining cash for 20% down payments on three additional rental properties.

I’m tempted by the peace of mind of owning all of my personal assets free and clear with zero debt, however the math would clearly say leveraging multiple properties at sub 3% interest rates would leave me with a higher net worth in the future (albeit I expect higher risk as well).