Quality is a big factor especially for broadcast bitrates, QuickSync has superb quality even at low bitrates better than even Turing NVENC which is top notch and much much better than Pascal.
I doubt the Texas Instruments chip you found can do transcoding, it probably can only encode/decode.
44 streams of 1080p30 for h264 to h264, ofc you can select any resolution and frame rate you like.
Intel's white paper (https://www.intel.com/content/dam/www/public/us/en/documents...) says up to 12 per CPU.
The card uses 235W.
A consumer security DVR can record 16 channels at for $100.
I found a TI chip from 2011 that could encode 6 streams at 1080p30, about 10W for $100.
The biggest advantage I see, as you pointed out, is the fact intel did all the software work and it's practically drop in.