It really depends. If you want to pay 100% cash for a home then yes, high interest rates are the best time to buy. But with interest rates currently below market returns, you're maybe best off borrowing 80% and using your remaining cash for a diversified portfolio of liquid investments that will likely outperform your APR long term.
If you view homes as day trading then yeah, there's risk in interest rates. But it's a home - a place to live if it's a primary residence. Ultimately if interest rates go up I don't really care since I don't plan on selling anytime soon. It doesn't change MY monthly payment. And if I did want to sell, well I'm staying in the same market - housing. So prices would drop across the board. So yes, maybe I can't sell my home for much profit or even a loss, but my home isn't the only one affected by this. Because you're in the same market, whatever you trade it for will have suffered a price drop as well.
Likewise if you buy a home while interest rates are high and they fall. Your home will have gone up in value but so will any other home you want to buy. So you're in a similar situation.
So I'm not worried about tail risk here. You do expose yourself to risk, however, if you buy more home than you can afford and we run into rough market conditions which put your income at risk. If you can't cover until things improve then you end up like the many people in 2008/2009 that lost their homes due to being over leveraged (mortgages are leverage, after all). This isn't unique to homes, however. Margin has its risks.
Here's how I see it, and I realize I'm fortunate: If interest rates begin to rise considerably over the next decade, reversing the trend of the last 40 years (!!!) then I'd consider pulling a portion of cash from certain investments to buy a home with cash after selling my current home for whatever p&l I get - if I want a new home. Or I'd just continue to live in my home and not worry about it. After all, I view my home first as a place for my family to live comfortably and then secondly as something I could make a return on one day maybe. But that isn't my primary concern.
If anything, I'd probably stay in my current home and then buy a second home (a vacation home, rental, etc) with cash.