I am currently working with DENV, I will just share some of my thoughts.
1. Since I am working in Singapore, local context is one of the reasons. DENV1 and DENV2 are the two major serotypes circulating in Singapore for the past ten years. The major circulating strain has switched from DENV1 to DENV2 since 2006. DENV3 is occasionally found, DENV4 is rare in Singapore. I am not very sure about other regions or country.
2. It seems like DENV2 is the serotype that can well grow in mice compare to others. For the past few years, most of the animal model only using DENV2 as it can give viremia or other readouts. Only until recent years I think is 2016, the community has reported a DENV3 and DENV4 clinical isolate that can cause clinical manifestations and replicate well in immunocompromised mice.
3. This is my personal guess, it might be because the marketed vaccine Dengvaxia has lower protective efficacy in DENV1 and DENV2 serotype, that is why more efforts have been invested in studying DENV2.
Let me know if I said something wrong or illogical.