Or that properties in rural areas within driving distance of a major airport may be less expensive currently but are likely to rise in value and therefore be a good investment?

Cut the supply in half, and rising prices were the only logical outcome.Now in addition to an inventory crisis, we have an inflation crisis with material costs increasing immensely and quickly, which will and is leading to further price increases.

In a posh high rise.

Is there even demand for this for apartments in Chicago in non-high or mid rise buildings?

As others have mentioned, it may tank next month, or it may continue to rise; it is volatile. 

The rates are rising and you should discuss the prospects of the future rates with whomever you work with for the policies.  

Inflationary preasure is not just being found in housing....it's in materials with wood up 500%, steel up 200%, used car prices up 52%.And it doesn't matter why prices rise...rising prices by definition are inflation.But dont worry, because the cost of transportation services has plummetted, every factor in CPI is way up, but transportation services is way down creating an average that makes it seem that inflation isnt there. 

Is it even possible to BRRR if this home value plummets & the interest rates rise.

This can be a great way to pick up anywhere between 5-10 units in your price range in one transaction.It's widely expected that this market will continue to rise, or at worst, level out and hold steady.

Rents are rapidly rising in most major markets.