That's correct to an extent.
I have seen a lot of leadwire burning from high powered burps, as well as just being yanked apart when they are set up with different styles of leads. Things like smashing the leads inbetween the spiders, free flloating them, etc can also cause undue stress, friction and heat to be applied to the leads.
Being sewn down reduces the movement of the lead itself. Just keeping them from flopping all around, smacking into the cone and spiders makes a world of difference. In most cases, up to twice the power handling from the start vs free floating leads when using the same size and amount of leadwire.
When they are smashed inbetween the spiders, friction is a killer. Heat builds up, burns the spider, etc. Not to mention that when placed inbetween the spiders, the leads are not allowed enough length to stretch under high excursion, causing them to be completely ripped in half!
This way also causes non-linearity in the spipder itself. No matter what anyone says, a bunch of wire smashed inbetween the spiders has a big effect on the suspension.
As for the coil to lead connection, you have to remember that this happens in a region of the speaker that does not move. This connection is made and then glued in place. The coil itself is more or less a hunk of material. It moves as a whole, but the small individual strands make up and entire unit. If the actual strand of wire was under stress from movement, friction, etc, then sure.
The leads are under high amounts of stress at all times during play, therefore they need to be a lot more resistant to these conditions.