This species also does start new growths from the base rhizome, as any sympodial orchid, but with the growth habit you describe there really is no distinction between a branch and a keiki. Makes it a very easy species to propagate.
Yeah they just kind of throw off branches/keikis everywhere. If you want it to go to a dedent size just leave them on there and let is spread. I just remove any that break off on their own or to 'tidy' the plant up as it can end up looking messy after a while.
Let it grow! It will use the roots from the 'keikis' to hold onto the mount. I agree with keeping the very old dead canes trimmed or it can lead to a big mess.