It is/was not uncommon to see wo teardrop shapped adheasive on speaker cones. This was to cover the wires as they come up through the cone and down into the voice coil. Example
However, I have noticed that I have not seen that as much recently. I assume as it became more common to have removable grills, designers decided that the wires and goop didn’t look very pretty. Apparently they are able to make speakers just fine without pushing the wires through the cone. Example
Why did they do it in the first place? Was some development made to make it not necessary any more? What are the tradeoffs involved?
I suspect it’s just evolution of design and someone figured out how to bring the voice coil wires out via the spider instead of along the cone.
Why was it done before? It’s easy. Run the wires out from the coil, poke the flexible leads through the paper cone, quickly solder the connections, seal it all down with a bit of varnish. Why did they stop? “Exotic” materials like polyester cones, silk domes for tweeters, etc. won’t survive soldering.
There’s a picture here:
speaker basics (ht-audio.com)
…showing the wires going through the cone, but under the dust cap. I think that’s more likely than going through the inner support ring.
I think the reason the wires come in from the inside is because the coil is wound on the outside of the former, and has to be very flat and even, and there isn’t room to free wires, which would be subject to magnetic movement and stress. That’s only an opinion.