Tannins are always extracted and they are actually needed to precipitate haze.
I think that a lot of brewers forget that tannins are always
extracted. I like to see substantial Oberteig in the mash tun, which I interpret as good precipitation of polyphenol-protein complexes in the mash, where most of this precipitation can occur.
How low are you talking about for the calcium? I had about 60ppm Ca.
I have recently tried a number of lagers with calcium concentrations in the 30-45 ppm range, after a number of prominent brewers suggested that pale Lagers can benefit, flavor-wise. Usually I would shoot for 50-75 ppm for a Lager I don't think there was an obvious flavor improvement, but the beers cleared slowly. They have required about 2-3 weeks of lagering to clear, despite being clear at the end of fermentation, where my lagers are usually crystal clear after 1 week in the fridge.
It's possible that the slightly higher pH, from the lower calcium, is the culprit not the calcium per se