I was looking for a quick reference to the push-pull design and stumbled upon this post. Couldn't help but notice that your design isn't a true push-pull amplifier.
Consider that you want to drive a very powerful speaker (nominal impedance is <10 Ohms) but your starting point is an op-amp with high-impedance output (>1k Ohms). The point of making a push-pull between the two is that both transistors are connected in the common collector configuration and thus, they provide very small output resistance (~1/hfe or ~1/hfe^2 with Darlington design) and near-to-unity voltage gain (because the b-e junction is in forward high-injection). On a minor side, through careful (but achievable - see below) biasing, you can remove any non-zero DC bias at the output port, which will destroy the speaker in the long run by heating it up constantly; and, you can remove the cross-over distortion due to the required base-emitter voltage drop. Overall, a push-pull design provides high driving capability without a transformer, which is bulky and has a pass-band limit.
In a two-stage amplifier with an op-amp providing voltage gain (high output impedance, nearly zero output current) and a push-pull giving current gain (low output impedance, unity voltage gain), you can use the final stage (push-pull) output as the feedback to the op-amp, thus making the output stay at zero all the time. To bias the base nodes, you can use a pair of diode-connected PNP/NPN transistors of the same part number; Further optimization can be done to give you a true class-AB amplifier.
In your circuit, the two transistors are connected in common emitter configuration. This is not getting to the point of a class-AB amplifier. The output resistance of a common-emitter amplifier is rather high (indeed the "better" the transistor, the higher the output resistance, as it's determined by the base width modulation which is more significant when a higher hfe is desired). It cannot be used to drive a low-impedance load, or at least with decent efficiency. Since you have heard it loud and distortion-free, I suspect that your load isn't powerful enough to expose the limitation of a common-emitter design and thus warrant a push-pull. Try a 4-Ohm or 8-Ohm power resistor instead, and use an oscilloscope to look at quantitative measures, spectrum & distortion as such.
Furthermore, when the two collectors are tied, there is no guarantee that this node stays at 0V at rest (quiescent point). First of all, the collector voltage in forward active mode is nearly constant versus current, and so a small change in the biasing resistor will cause a large shift in output DC level. Compounded with process variation (extrinsic factor) and electron-hole mobility difference (intrinsic factor), it is nearly impossible to reliably achieve 0V DC bias. If you feed it back to the op-amp stage, which is feasible in the previous case, it may require an op-amp output beyond the voltage rail. With the non-zero quiescent voltage, once you connect the load, a constant DC current will be heating it up. Even if it's not that extreme, your total voltage swing without distortion, and therefore maximum output power, is limited due to the reduced headroom. These process-dependent results may not be easily observed in academic/theoretical simulations, as all models/parameters are too idealized to reflect the reality. So, just use an oscilloscope.
There are practical use cases for tying up the collectors. Actually, it's more common nowadays to use CMOS transistors. One side serves as the actual amplifier and the other side provides high impedance (from the drain port) with a relatively low drain-source voltage drop (lower than a transistor-resistor design with comparable voltage gain).
In other answers, @oneprivate and @Adam Haun mentioned power transistors being slow, at least in the past. I'm not knowledgeable enough in audio amps to understand the historical reasons for these design choices, but IMHO you can improve the frequency response by transfer function engineering. Power transistors are generally "slow" as the input-output coupling capacitance is generally large, which is further amplified by the Miller effect (forming an additional low-pass/shunt capacitor at the input port). So I guess .. you will want to separate the voltage and current amplifying stages?