I don't think I've ever seen a transformerless push-pull power output with emitters towards the power rails. That would mean the speaker at the collectors and collectors are high impedance points, ie current sources not voltage sources. Not what you want for directly driving apeakers.
Every rail to rail output opamp works this way, and some are specified for audio use under substantial loading, like driving headphones. If there are any rail to rail power amp chips (I dunno) then they also need to work this way, obviously.
I too used to think that output impedance would be horrible, but I don't think so anymore. Oftentimes Miller compensation is included around the output stage, which AC couples the base to the collector, so that any collector voltage swing results in similar base voltage swing (mind base-emitter capacitance, though). Such stage ought to have only slightly worse output impedance than an emitter follower at high frequencies, and at lower frequencies the global loop takes over controlling the base to regulate appropriate output voltage.
Case in point, TL431 has a Miller-compensated common emitter Darlington output stage which is current-driven by the earlier stage. The whole thing operates at a few mA (the earlier stages at sub-1mA combined) and specified output impedance is fairly low and flat to 100kHz. It is also stable with capacitive loads up to a few nF. Unfortunately, more interesting ICs like opamps don't have their schematics disclosed in nearly the same detail.
I think common emitter outputs aren't popular in discrete amplifiers mainly because there is no pressure to maximize output swing on very modest supply rails and because they are harder to bias into push-pull class B than complementary emitter followers. The circuits used in opamps seem to vary from "meaningfully more complex than a Vbe multiplier" to "way too complex and finicky for discrete builds". I think the most promising approach could be the one devised by Monticelli at National Semiconductor long ago, which can be seen in contemporary OPA211 datasheet. It is analogous to a traditional bias spreader for Darlington EF output stages split in two halves and connected to supply rails, which means it should have all the same thermal coupling problems as the traditional solution and hopefully no other thermal problems.
NE5534/5532 famously has an NPN/NPN output stage. I think this could be reproduces in a discrete amp, if the diode which permits the VAS to sink load current is thermally coupled with the bias spreader (or part thereof). Another clever solution for NPN/NPN was given by John Linsley-Hood in his class A amp, but I think it's only good for class A.
Then there is the whole world of amplifiers with Sziklai pair output stages. But despite the use of common emitter power transistors, they are fundamentally voltage follower output stages and not much different from Darlington pairs. Some controversies seem to exist over which is better, both in terms of THD and bias stability.