I used to keep them under Starsan for a few hours after brew day. That "chalking" appeared after accidental prolonged submersion in Starsan, like 3-5 weeks or so, I simply forgot to pull them out. I scrubbed the white haze off, and pumped hot PBW through them. I see no degradation whatsoever. No brittleness either.
I'm with you on that, I don't think it's the Starsan per se, unless the tubing the OP uses is not Starsan resistant, which may be the case.
I keep a small container filled with Starsan with short pieces of vinyl tubing used as adapters, silicone stoppers, racking cane inverters, oxygenation stones, and a 3" piece of that 1/2" thick walled silicone hose. That piece of silicone hose must have been under Starsan for over 6 years by now, except for short uses in between, when bottling or filling growlers.
That piece is as pliable and transparent as a new hose while all the pieces of vinyl tubing are opaque, but will clear upon drying, and many plastic pieces have lost some of their color.
On a side note, those silicone hoses I use are the Platinum cured type I got about 7 years ago.
I've had both the clear vinyl tubing and silicone tubing develop issues. The vinyl tubing became slimy, the silicone developed the white haze on it as you describe above.
I still sanitize tubing w/ Star-San, but it's just a dip and a drain. No long-term soaking. Frankly, they don't need more than a dip unless they're not cleaned properly--and if not, then they need to be....cleaned properly.