We assume that weights need to be continuously updated because that's how lay people imagine the human mind to work. But even the human mind (most likely) doesn't learn continuously: there is a consolidation process that happens during sleep.
So in some sense AI learning is already not that different: latest data from short term is consolidated into long term memory. It's just that for a person this happens nightly and for an AI - quarterly. And the short term memory is that person's experience vs the entire Internet.
And whether something is lucrative or not is decided by utility and price, not how the technology is put together.
1) No-one is suggesting that an AI should only learn from a restricted set of data - but rather that it should continually improve itself based on new data, observed or committed mistakes, etc.
2) No-one is mandating how or when the ‘consolidation’ takes place - just that it would seem to be better if it did, somehow, more regularly and reliably than via training of a new model generation. “Continuous” doesn’t have to mean every millisecond - it could be analogous to human learning, with a step-wise incorporation of short-term memory (context) into long-term memory (weights).
AI that remembers through continuous experience instead of documents would be significant and lucrative enough to change the business model.