Real estate is a risky and illiquid investment. As rates go up, it becomes a less desirable investment. Real estate also requires large cash outlays to acquire. That means that most acquirers of real estate must borrow the funds to acquire it.
As rates move higher, mortgage money becomes harder to get and the cost of carrying the investment real estate goes up, also making real estate less desirable to hold as an investment.
You are commenting mainly on the fact that the single family residence market did not suffer as much as would have been expected. But single family residences are not investment property as its primary purpose. And residential real estate may move contra cyclical to the investment real estate market because of demographics.
Finally during the 70's, investment real estate was being distorted by the then existing tax code which allowed a lot of deals to be done via limited partnerships.
As you saw, investment real estate gravely suffered when Congress changed the tax law. And that suffering took a long time to work out of the system. Just remember, at any particular point in time, different factors may be taking place that distorts what would normally be expected. The 70's was a period like that because of several factors as already mentioned; i.e. special demographic circumstances coming together with tax rules, as well as others that did have investment real estate reacting to basic economic factors differently then would have normally been expected.
There are many factors that could affect real estate, but in simple terms, when interest rates rise, demand for money falls. Demand for home mortgages probably is directly affected, and thereby home sales, and so residential property prices should fall, OR perhaps just not grow near as fast, OR just stagnate. I know in my neck of the woods, the combination of a major company laying off several hundred six figure earners and rising interest rates have made home buying in the better neighborhoods EXTREMELY attractive.
There will always be exceptions (like you mentioned, along the coast. I've been looking for a beach house, and they prices rise while I look!). Even the case Skip mentioned wasn't much of an exception. Sure, rates were increasing, but inflation was high, too. The Fed raised rates until it got inflation under control. As soon as inflation began to subside, the boom in real estate ended.