Tinned how? Stranded tin-plated, or the whole thing has been dipped in solder or something, or just the ends done up?
Seems like I only ever saw the fused stuff in old equipment, maybe they dropped it for a reason.
Plated, loose strands are fine in whatever.
Soldered ends in springs, I don't see why not, just the issue noted: it's a stress raiser.
Mind that conformation to the spring, may be a false economy: at idle it fits tightly, but under just a little vibration (and there's a lot of leverage on the tinned section due to its stiffness), it'll skew in the spring clamp and suddenly the contact area is much less. It should still make contact, I think I would be surprised if it's a problem for signals but under power loads (some amperes) maybe it's not such a good idea. Or maybe solder will contact-melt under such conditions and it's really not much of a problem (it solves itself within some tens of milliseconds say)? Dunno.
There's also fretting corrosion, which I guess shouldn't be a problem for most any solder in brass or tin-plated contacts, but discourages gold-plated contacts.
In other situations, I've seen solder give just absolutely terrible contacts, like I made a single-AA flashlight a long while ago, using a solder bump for the negative contact (a spring for positive). It has no end of a cruddy connection, easily seen by shaking or rolling around the battery. It must be something like, the solder is so soft, it rubs off easily, and the particles get stuck in the gap, increasing resistance considerably (and this is at voltages and currents where it's not really going to start any nonlinear processes like point remelting or something). Probably aggravated by skin oils or whatever, making a colloidal suspension perhaps (it doesn't take much, a fingerprint amounts to a microns-think film of oil).
But that should be avoided by the higher contact pressure -- those terminals use a shearing sort of joint and stiffer springs than my flashlight thingy.
Tim