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You've already got a pretty good understanding it seems, as you're pretty much right on with most of your speculation. With class B and AB amplifiers it is pretty much standard operating procedure to use push-pull pairs, but with class C it's actually rare outside of CB amp setups. Most class C arrangements  that I've seen in commercial and amateur designs are single-ended and many of them use several single-ended stages in parallel, but usually no more than three. By my logic though (and this is speculation) a push-pull class C amp will have slightly better linearity than a single-ended class C amp simply because the 2 transistors together still produce a more complete waveform than just one transistor in class C. The CB amp folks use push-pull exclusively, but many if not most transistor CB amps do not have any bias on the transistors, making them class C amps. The IMD performance would still be as described in the device datasheet (if specified, many have no published IMD spec) as long as the transistors are not being overdriven, and any harmonics could still be taken care of through filtering in commercial and amateur designs.


Also, push-pull designs have an inherent benefit: The design naturally results in a suppressed 2nd harmonic. You've still got to deal with the higher harmonics, but the 2nd harmonic in a single-ended design can be quite powerful and difficult to filter so it's nice to have it naturally suppressed. Also this inherent suppression is what allows for broadband HF amplifiers to utilize only 6 band-switched filters instead of needing a separate filter for each band. This applies to ANY push-pull design regardless of class, and this is why class B and AB designs are almost exclusively push-pull. I think that the choice between single-ended and push-pull when dealing with class C is a matter of cost and efficiency. Because of the efficiency provided by class C operation, a single device can go a long way and not generate too much heat. There is substantial cost savings if only a single transistor can do the job, and the added cost of filters with sharper cutoff to deal with the strong 2nd harmonic isn't so much that the cost savings are reduced much.