There have been a bunch of good answers from other people, so I'll take a different tack.
I'm not sure the question needs to be "philosophical"...I think it really just boils down to a question of mere survival. If it wasn't for the fact that Sigma made lenses for other brands, there probably wouldn't be a Sigma! ;-P I mean, when you get right down to it, Sigma's cameras have basically "nil" for market share. Of the total camera market, Canon, Nikon, and Sony command some 87-92% (depending on which years data you reference, from the last 10 years). On average, there has been about 11.5% "other" market share, and from that 11.5%, Sigma doesn't even come up in any searches, graphs, charts, or tables, indicating it's share of that share is only a few percent.
Without lenses, Sigma's ~1-2% market share in cameras wouldn't be enough to keep them alive. They wouldn't have any money for R&D of any kind, let alone for lenses. Sigma is a lens company first and foremost, and they have become a good lens company. They are a camera or general photography company a distant second.
So, why does Sigma make lenses for other brands? Because
THAT is their business: Lenses.

(Just to be clear, I'm not bashing Sigma for this. I applaud Sigma for moving beyond their prior status as an "Decent" lens manufacturer in years past, and have moved into the realm of "Great" lens manufacturer. It's just that, quite simply, that's what Sigma is...a lens manufacturer. They aren't really a full blown imaging company like Canon or Nikon...who's core businesses involve several lucrative divisions and large, broad R&D departments spanning multiple markets from medical to industrial to cinematography to photography. Sigma's primary business is lens design and manufacture...so it's no surprise they produce lenses for third parties as well as their own cameras.)