My experience has been almost the opposite. For the most part it didn't matter which cables I used, they all went out quickly. I tried the super cheap, OEM brands, and everything in between. For a time, it was actually more cost effective to buy online cheap cables in bulk even if they went out quicker. For the most part, the cables are all the same design, so I don't see any real safety issues with using random brands.
There have been two exceptions so far in my experience. I bought some from Dollar Tree and that one must have had very thin power wires. Even brand new, they wouldn't handle full current. I couldn't actually change unless I flat shut the phone down. The other exception is my current cables. I'm using some Volutz brand cables that I got at a reasonable price from Amazon. They have held up well so far and they look nice. I did have to exchange a couple, but the warranty process was relatively easy. The replacements and the other three originals are still holding up well.