That isn't really true. The carnot cycle does operate between two temperature sinks.
The carnot cycle is merely a cycle which assumes that there is no increase in entropy due to imperfections. It is useful because it is the pinnacle of thermodynamic cycles and it can tell you thinks like the maximum efficiency any cycle can reach when operating between two given temperatures. It isn't used because it cannot be achieved, it just isn't possible.
However, the stirling cycle is implementable and has a maximum theoretical efficiency which matches the carnot cycle. Stirling engines are used in a few applications, like a stirling cryocooler, successfully. However, it is generally more practical to use mechanical devices which run on other cycles like an Otto cycle (automobile) for example.
I know there are two different temperatures but the heat transfer takes place isothermally which is physically impossible.
So that is different than isentropic because no imperfections which off course is a requirement that also needs to be met.
There is isothermal expansion, adiabatic expansion, isothermal compression, adiabatic compression. I should have stated more clearly that there IS a heat source and sink which are at different temperatures.
These are always interesting discussions. However, even do a saturated liquid can absorb heat isothermally, there still needs to be some kind of gradient at its boundary to get the energy into the saturated system, whether heats enters through conduction, convention or through some radiative means. Holding a source against the body of interest at equal temperature simply will not produce any flow of heat. Even in theory this would happen at an infinitesimally small pace. That is why Carnot cycles cannot operate in real life.
As stated in post 3, the defining characteristic of the Carnot cycle is the lack of a change in entropy through the different processes. This isn't just a matter of friction in parts, but there is entropy lost due to the behavior of the working fluid itself.