I think you're confusing a few things.
First, upscaling with a filter kernel (weighted average) doesn't make as much sense because you aren't weighting multiple pixels to make a single pixel, you are interpolating, so "upscaling with a triangle filter" isn't something practical.
Second, lots of signal processing things that can be technically applied to pixels on a row by row basis don't work well visually and don't make a lot of sense when trying to get useful results. This is why things like a fourier transform is not the backbone of image processing.
Polyphase filtering doesn't make any sense here, you have access to all the data verbatim, and you want to use it all when you upscale or downsample. There is no compression and no analog signal that needs to be sampled.
Third, any filter kernel is going to use the pixels under it's width/support. Using 'too many pixels' isn't something that makes sense and isn't the problem. How they are weighted when scaling an image down is what makes sense. If you want a sharper filter you can always use one. What I actually said was that linear interpolating samples to downsample an image doesn't make sense and is like using a triangle filter or half of a triangle filter.
This all seems to be work arounds for what people probably actually want if they are trying to get some sharpness, which is something like a bilateral filter, that weights similiar pixels more. This