I work tech support for a NAS company and the ratio of HDDs to SSDs is roughly 85-15. Sometimes people use SSDs for stuff that requires low latency, but most commonly they're used as a cache for HDDs in my experience.
Not sure whether adding more power consuming devices results in less power consumption, though. I guess it depends on drives power usage and files use.
Smaller doesn't matter if they're going in a 3.5" tray. There are some models that only come with 2.5" trays, but go figure, the only 2.5" model that isn't a 5-figure all-flash enterprise-scale model is one of our least popular models
If the NAS supports tiered storage, you benefit from high I/O performance for things like video editing.
My home storage is a NAS connected over 10GbE, I never bothered trying to play games off of it, but I'll bet they'd run great. Read & write over the network at 10 gigabit is faster on a machine with (separate) RAID arrays of SSDs and HDDs than internal SATA3 connectivity which is kind of bonkers for a home user. Plus that has virtual machines and cloud backups running on the NAS side.