That's right - a sufficient amount of genetic diveristy is required to differentiate phylogenetic taxa/samples, however, "too much" divergence can also introduce artefacts. One common example is long-branch attraction, when using an outgroup that is too divergent from the assumed "ingroup". Highly divergent data can also lead to inaccurate recombination estimations.
In RNA viruses, recombination occurs during replication where the template strand is swapped out for another one before its completed (copy choice mechanism). This produces a recombinant. Traditional phylogenetic models assume that one sample has one origin. A recombinant has more than one evolutionary origin and can violate this assumption. Depending on what genomic region you're looking at, it could be more similar to a distantly related genotype and distort the topology and branch lengths of phylogenies. Failing to account for recombination has also been shown to affect other evolutionary inferences.
Recombination is definitely not a one-time event. Similar to mutation rate, different organisms have different ranges of recombination rates. Generally, positive-sense single-stranded RNA viruses (coronaviruses are one) have a lower recombination rate, whereas viruses like Influenza and HIV are highly recombinant. The interplay of recombination and mutation helps generate genetic diversity in a viral population.
To emphasise how recombination isn't a one-off occurrence - historically, studies have elucidated recombination between genotypes, lineages or hosts. A recent SARS-CoV-2 study identified ancient recombination events to help understand the evolutionary origins of the virus. More recently, deep-sequencing of viruses have shed light on recombination that occurs between viruses within a single host. It's still quite difficult to analyse within-host data due to the high similarity between sequences, somewhat similar to the issue with low mutation rate confounding a phylogenetic signal.
Overall, recombination remains biologically and computationally complex. As the Nextstrain team have alluded to, further development of methods are required to account for recombination between highly similar sequences, as much as being scalable to process the immense amount of sequences available (e.g. ~ 60,000 global SARS-CoV-2 sequences).
Hopefully some of this is helpful! I've included some references throughout for further reading :)