You got bogus information. The HDSI transducer is 2" longer.
CS will tell you that you cannot use 800 kHz with the Compact SI transducer either, but you can.
You can connect the Compact SI transducer to the higher end models and loose some image clairty and you can connect the HDSI to the lower end models and gain some imaging clairty.
Been-there-done-that, got the T shirt.
When I just had one SI unit, I used both transducers several times a day since I swtiched the display between the console and bow.
I have several HDSI transducers, a couple of Compact SI transom transducers and a Compact SI trolling motor puck. Plus a unit that is 455 kHz for Side Imaging and units that are 455/800 kHz Side Imaging.
It's all about the length of the SI crystals and the thickness of the sonar pulses front to back.
Same unit with the two different SI transducers. Not the same location, but you can get the idea since both are of a creek channel.