Why don't modern jet engines use forced exhaust mixing?
Source: wikimedia.org

They're back. Above is the General Electric Passport. Entry into service was 2018.


  Its core cowling, exhaust cone and mixer are made in ox-ox composites, with inorganic high-temperature-tolerant resins and oxide ceramics CMCs to withstand 1,000°C without deformation, saving weight and allowing complex molding.


The above hints at the hotter exhausts of the newer (since the mixers disappeared) engines, and that CMCs were the solution.

For the turbine inlet temperature, below is the trend:


Source: researchgate.net

From the respective flight manuals, an A380's max continuous EGT (Exhaust Gas Temperature) is 970°C, while it's 580°C for the older MD-80 (both don't have mixers, but it shows the trend). While you can bleed-cool turbine blades, there must have been no gain in cooling a mixer with bleed or they would have done it (bleed takes away from a combustor's efficiency, and at some point overall gains turn into losses).



Related: Why did Boeing remove the engine chevrons on the 777-X?