The big robot will survive in large scale manufacturing for the same reason Java survives in enterprise; it's part of the culture at this point. It does its job well, it hardly ever fails, and it's relatively easy to bring someone up to speed on working with them. Like Java, you'll probably see a number of companies pop up that prefer a newer technology, because it fits their use case well. But I'd expect the bulk of total money spent to continue to be on the kinds of industrial robots we work with now.
The place I can see small robots making an impact is knowledge work, such as laboratories or design. And realistically, in those fields we've never been time constrained. It's more common, in my experience, that the limiting factor is the number of good ideas a person can come up with. There's no way to reduce "hours formulating an idea" short of AGI. Scientists have to read papers, designers have to study a company or product to make all of the branding coherent.
All of that said, the newer, low cost bots will probably move the needle, but they won't accelerate the pace of automation significantly. More likely, they'll contribute to maintaining the current acceleration.