This has been a subject of a lot of experimentation for me.
I generally agree that unless you're shooting stills or crop modes, lens resolution/sharpness really isn't a factor since 1080p is such an incredibly low resolution. Especially considering the detail that all still lenses are engineered to produce on full-frame film.
But there are a lot of other optical qualities that you get from a lens in it's overall rendition like contrast, flare, bokeh. These differences are apparent if you cut with from a high contrast lens like a Zeiss prime (well, ok, *many* Zeiss primes) to a lower contrast Leica or Canon. This is especially noticeable with a human subject. With all of the data that we get in 14-bit raw, yes you can very easily adjust the contrast but those two shots will never look the same no matter what you do. The point is there are difference between zooms and primes in these qualities.
There is a lot of mention in this thread of new Canon L autofocus glass. I have the 24-70/2.8L (edition I), 70-200/2.8L (non-IS parfocal), 50/1.4, all EF autofocus. They don't get used much because it's absurd trying to pull focus with them, I don't like camera-controlled < 10 blade aperture, and the crisp & clear look isn't what I prefer these days, it's too perfect. All of that convenience is ideal for stills, though. I hope I'm not off-topic here, apologies in advance...
The problem is that the selection of autofocus zooms that are also parfocal is very slim. The opposite is true with older manual focus lenses.
I have a set of Vivitar M42 lenses, a set of Russian M42 lenses, a Canon FD set (thanks to EdMika on ebay and his adapters), scattered German, and an assortment of antique lenses for experimental use. Collecting vintage glass to adapt to ML raw has become something of a hobby. The only potential drawback is a time investment in finding the right adapters, and any cost you may face if the copy you're buying needs cleaning, lubricating, possibly declicking the aperture, etc. IMO it's worth it. I should get my act together and post samples at some point.
Anyway to get back to the OP's question, the # of lens elements of a zoom is large, so in addition to what's been said about how they resolve differently, the flare of a zoom will never look like that of a prime. You almost never want flare in a still photo, but I see it a lot in film, and it's usually intentional.