Most blue ray players with usb2 actually use it in full, meaning the data transfer rate can be more than 33 mBytes/sec when playing large HD .mkv or .m2ts files (more than 2 Gb or even 15-25 Gb). That's practically imposibble to achieve through normal usb2 connected HDD to them. But surprisingly well this smooth play of huge files is achieved using ANY usb3 device attached to them via their usb2 port. Some Sony devices support even 3Tb usb3 HDD. In other brands such as Samsung that can be achived through 2Tb max HDD or by splitting into partitions a HDD larger than 2 Tb. Obviously the default file system supported on those HDD is NTFS to support such large files. So far exFAT is not yet supported by usb2 endowed TV, blue ray players with build-in ability to play various video formats: mkv, mp4, xvid or more seldom today divx avi, mov, wmv, mpg, m2tv, vob files or more rare ones.
Obviously no wi-fi can support that data transfer speed or even wired ethernet network [those devices support only 100 Mb not 1 Gb ethernet as by default today laptops do].
No cheap (less than $200) blue ray player support eSATA cobnnection. No usb3 TV or blue ray player are sold yet!