Um, NO! There is NO requirement for calcium in brewing water, but there are a couple of good reasons to have it in there.
The malt provides ALL the calcium that the yeast need for their nutrition, but having ionic calcium in the water can provide a couple of duties. The first is to react and precipitate oxalate out of the wort. You should have about 40 or more ppm in the MASHING water to produce that reaction. The sparging water can have zero calcium. The other reaction that you'd want ionic calcium available in the mashing water is to improve mashing enzyme activity. A final reason a brewer may want ionic calcium in their mashing water is to produce its pH lowering effect by reacting with malt phytin.
Those reasons can be assessed by the brewer, but an important point is that many of those actions are produced by dosing the mashing water with the calcium salt and not the kettle. It does not appear that adding calcium salts to the kettle instead of the mashing water is really wise.
While all those reasons mentioned above are useful, that is not to say that every brew should get a healthy dose of calcium salts to promote them. Sometimes, its more beneficial to the beer to have a lower ionic calcium content. This is particularly true for lager yeasts since they are susceptible to premature flocculation if the calcium content is high. Since lager yeast need to stay in suspension for a while during and after fermentation to perform important flavor and off-flavor improvements, keeping them in the beer is helpful. But for ale brewers, the opposite can be true. Having 50 or more ppm calcium helps clear the beer earlier and get it ready for serving sooner.
To provide low calcium content in lager wort while still temporarily boosting the calcium content during mashing, adding all of a batch's calcium salts to the mashing water and none to the sparging water is the way to go. Of course, this assumes that you're starting with very pure water like distilled or RO. The supporter's version of Bru'n Water is set up to provide for that technique and I find it works well in producing great lagers with low ionic content.