They don't have to catch up, they just have to be good enough on a narrow set of tasks to be worth the trouble. Perfect is the enemy of good here. Everything I've seen suggests that the prototypes are already pretty good at simple tasks that involve recognizing, picking up, and putting things into/onto other things in some way.
All the dancing, jumping, running, etc. is nice for marketing but not actually that urgent for such tasks. Dexterity is nice. There are plenty of examples of humanoid robots doing pretty fiddly stuff like folding t-shirts and other things.
The rest is just optimization where these things gradually get faster, efficient, do more complex things, etc.
> they just have to be good enough on a narrow set of tasks to be worth the trouble
Depends on the context. If they are to work around human beings, particularly in the home, then they must be safe... to work around humans.
If a humanoid robot hits a human being, knocks one over, or even falls down on top of one -- especially a child, who is more fragile and whose movements are unpredictable -- then the industry as a whole faces a huge setback. Just look at what happened when a "self-driving" Uber ran over and killed a pedestrian in Arizona.
As always I feel compelled to say that the bar is not "never hurts a human being." It's "hurts human beings less than the status quo." Home helpers, for example, also occasionally hurt human beings. Further, the elderly hurt themselves a lot doing chores around the house. If the sum of these incidents (in severity and frequently) is greater than the sum of accidents by robots, we should still use the robots.
I see similar arguments playing out in self driving. People point to the occasional accident and proclaim that the technology is useless. But the bar has never been "perfect." It has always been "better than humans.*The Danish and Dutch government transport departments recently ruled that the evidence is clear: Tesla self driving is now safer than humans.
All the dancing, jumping, running, etc. is nice for marketing but not actually that urgent for such tasks. Dexterity is nice. There are plenty of examples of humanoid robots doing pretty fiddly stuff like folding t-shirts and other things.
The rest is just optimization where these things gradually get faster, efficient, do more complex things, etc.