Why can't we extract more from exhaust gases in gas turbines? It is seen that EGT are of the order of 600°C (What is a normal EGT range of a jet engine?) for aviation turbines and nearly the same for stationary turbines. Why can't high temperature exhaust gases are further harnessed like adding another stage in turbine section that extracts more energy?

In aviation turbines can't we just add another turbine stage like another low-pressure turbine mounted on another spool? For land-based gas turbines we can somewhat utilize these high temperature exhaust gases in Combined cycle but what about aviation engines?
It can be done, but the better specific fuel consumption does not compensate for the extra weight. We all know that aero engines have to be as light as possible. In land, stationary installations, where weight matters but little, regeneration, intercooling, and even combined-cycle (in electricity generation, using a gas turbine that drives an alternator, but with the exhaust gases generating steam for a steam turboalternator, for example...). The efficiency is very, very high, but the weight and bulk are considerable, too...

But it has been tried: https://airandspace.si.edu/collection-objects/allison-t78-2-turboprop-engine

https://www.flightglobal.com/pdfarchive/view/1963/1963%20-%201880.html