The longer, the less safe, obviously (not just because of breakage, but also because of handling, the involved forces, and simply because there's a much longer blade protruding).
But if you respect them for what they are, and use them accordingly, they are pretty safe.
You will normally not want to use the full length of the blade. Except, you could maybe use it that way in a router table, but then you have to go very shallow. That is not the intended purpose of the bit, though. It's not a thickness planer!
The "normal" usage of these long bits is in a plunge router for a diversity of joints. But for obvious reasons, the bit is not intended to cut that depth in one pass.
Neither is your router powerful enough, nor would you be strong enough to safely hold The Beast if you plunged in full-depth. That's crazy.
Even with much shorter bits, one usually does at least two, more commonly three passes. With a long bit like this one, I'd do at least 6, if not 8 passes (6 passes is 12mm per pass -- surely OK for soft woods, but depending on what hardwood you're routing, that's quite a mouthful!).
I have admittedly seen people use 50mm bits to cut out the sink hole in 40mm kitchen benchtops in one go. Press button, plunge in full depth, and fiiiiiiouuuuuuu... Ah well, if you absolutely want to do that, you can. But of course, there's safer, more intelligent, less tool-killing things one can do. On the positive side, you're not likely to hit a knot in a kitchen benchtop...
About the actual length, and the shaft thickness: 3 inches are only 76mm. I have 96mm bits in my box which really feel a bit "uneasy" because they are so darn long, but I've never had a breakage (used mostly in oak and beech).
There exist bits that are 110mm (though I've never worked with any of these).
A 1/2 inch shank is pretty rock solid. I am using 12mm which is already close to indestructible (it doesn't seem that way, 8mm is not so much thinner and those can and will break, but there's worlds between 8mm and 12mm).
While 1/2 inch looks like almost the same as 12mm, those 0.35mm make again a big difference. It's over 12% more cross-cut surface (and thus tensile strength). Compared to a 8mm shank, it has more than 2.5 times the cross-cut surface.
You will obviously not want to use a bit which has a diameter smaller than the shank (doesn't help a lot for stability if the shank is 12.7mm but in the cutting section it's only 6mm!). But that's not normally a problem since tool manufacturers (normally) don't make such long bits that are thinner than the shank anyway.