Its not hard! I know of no tube pushpull tube amp with this problem unless it has a design bug. Its more something that can happen in a solid state amp if its biased so low its actually operating class C; IOW one output device turning off, then there's a slight gap before the other turns on.
IOW this sort of thing is a made up story; my surmise is its spread by people selling SETs. As I said before, its simply not a thing.
Now that isn't to say there might be something annoying about some pushpull tube amps compared to SETs. That can be caused by a number of factors, one of which has been known for over 60 years, which is that if the input circuit of the amp is single-ended and the output is pushpull, you can get more 5th harmonic, which just isn't all that musical. But that can be avoided in a pushpull design. The other problem, also avoidable, is improper application of feedback, typically applied the cathode of the input tube. That practice, which is still around due to tradition and nothing else, has also been known for the last 60 years to cause the feedback to make distortion of its own, making the amp less musical. This is because the cathode of any tube is not linear so the feedback signal gets distorted, which, if you want feedback to work, really shouldn't happen!
Crossover after the amp:
Pro:
the crossover is tailored to the speaker in many cases, often to deal with driver peculiarities. If the crossover isn't tailored in such a fashion the benefit is less.
Con:
1) In particular if you are running an SET, placing the crossover after the amp causes the bass energy made by the amp to be dissipated as a small amount of heat. Not the best use of amplifier power! Getting the bass out helps any amplifier, but SETs as I've mentioned before, are particularly susceptible to distortion if low frequencies are present.
2) Its harder on the power tube(s) since the output transformer in most SETs lacks the inductance to play bass properly, so even though you're not hearing it, at lower frequencies the load impedance on the tube is much lower than its designed for so the tube heats up, since more of the power its making is dissipated in the tube rather than the load. This can happen with PP amps too but its far less problematic.
Crossover before the amp:
Pro:
1) the amp is not receiving bass energy, so considerably more power is available at lower distortion to do its job with the mids and highs. This often means smoother with more detail.
2) Many people comment about the 'more immediate sound' when the amp is directly driving the speaker. No worries insofar as the output transformer is concerned.
3) The amp will run cooler even it its class A and the tubes will last longer. This is because the load line of the tubes will be more like the straight line its supposed to be.
Con:
1)the crossover might not be tailored for driver peculiarities. This may or may not be a real issue depending on the speaker.
2) an electronic crossover is an additional block in the amplification chain so noise and added distortion on its account may be audible. However some of the modern digital systems are quite good and allow you to tailor the response exactly to the driver.