I think new cartridges will still see adoption to a certain extent. However, in order to see very widespread adoption I think at least one of several things would have to happen, such as large scale adoption by a military, numerous LEAs, civilian shooters, or more than one.
Here are my predictions...I think...
.357 SIG - could gain popularity, especially if ammo prices and/or shortages arise again, which may lead some .40 shooters to consider a .357 barrel for hand guns with the ability to fire both. Many LEOs seem very happy with its real-world performance.
.380 - will continue to become more popular as more small, reliable, and affordable carry pieces come to market, as does advanced ammunition that works well with shorter barrels and the lower energy of the .380. If the future is more carry-friendly, this will be accelerated.
9mm - will only become more popular, as modern ammo has responded to the historic shortcomings that may have played a role in some shooters/organizations looking to other calibers
Perhaps something new between .32 and .380 for smaller CCW autoloaders?
.300 Blackout - will continue to grow because it offers a variety of benefits packaged into the AR-15 platform, ending in a versatile weapon that may get a popularity push from military adoption. It holds strong potential for personal defense, LE, and military usage.
.338 Lapua - with increasing presence within both armed forces and among civilian shooters, it's going to continue to grow, although the higher cost and amount of land needed to fully push it will probably ensure it never becomes the next .308
.338 Norma Mag or .300 Norma Mag - in the off chance that it is adopted as a machine gun round by any of our Military branches, it could take off and it seems like it could make a darned fine machine gun round to fill the gap between .308 and .50.