Weirdly, you may actually be able to get better terms and/or more LTV on the refinance if there is debt on the property as lenders have rules for max cash in hand (max proceeds you get at closing) for cash-out refinances.  

With a loan, a person takes on a Debt Obligation. 

Well, a lot of life happened and now I am getting back to zero no debt and I'll be renting for now and I am considering a duplex to buy cash or maybe land and some sort of unconventional home but still purchasing cash.

You may want to research the term ' Debt Financed Distribution' Which does have a tax implication for the investors receiving a distribution.

DSCR loans go up to 80% of the purchase price and depending on the Debt Service Coverage Ratio and your credit score you can expect rates on a 30 yr loan ranging from High 6%- Mid 8%. 

If you want to play a passive role, a real estate syndication or debt fund could be a great way to go.

Owning a duplex at 20 is a huge accomplishment, and it’s inspiring to see you’re already planning your next move.From my perspective, real estate investing is a long-term game focused on building equity, paying down debt, and maintaining stability over chasing short-term cash flow.

I am expecting to do 3-4 deals per year until I get to 20 properties or so and then snowball the debt so they are all paid off by retirement. 

Maintenance and potential repairs will also require a long-term financial plan and setting aside a contingency fund for such expenses.The steady cash flow, appreciation over time, and tax benefits can make a meaningful difference to your wealth in the long term, especially with the principal paydown on the mortgage.However, if managing the property from a distance feels too burdensome, or if you’d prefer the certainty and flexibility that comes with having less debt (especially given the high mortgage rates), selling and using the $100,000 in equity to reduce your loan for your next home may be the smarter move.

There is no requirement for @John Gillick to replace debt with new debt.