Why can't we extract more from exhaust gases in gas turbines?
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