You can capture VGA using all the same tools by adding in a VGA to HDMI adaptor. I haven't measured the impact on latency, but a few users have confirmed that it works.[0]
VGA capture has been solved for a long time by readily available products. You can get multi-port or single port units like the Lantronix Spyder. For the most part, HDMI has not had much of a solution. I suspect it’s because of the copy protection enforced by media companies combined with most sever companies moving to fully built-in management interfaces (e.g. IPMI, DRAC, etc.)