The DS could run COD if Activision was willing to put the time and effort into distilling that game down into something that can be played on a DS. The point is the amount of effort that takes, and it just not being worth that effort.
Let's put it this way. If it costs significantly more to port a PS4 game to Switch than it does to port it to Xbox one, while at the same time expecting significantly less sales, it becomes very difficult to justify that effort. If a port requires minimal effort than the sales that port needs to have to justify it is much smaller. This is where Nintendo missed the mark.
Porting COD to Switch is much less investment than porting COD from PS3/360 to Wii, yet that was done several times and was profitable.
More demanding games than COD have been ported, so the failure squarely lies with Activision.
"Porting COD to Switch is much less investment than porting COD from PS3/360 to Wii, yet that was done several times and was profitable."
Source? Or is that just an assumption?