Object manipulation has potential products in dishwashing and vegetable chopping - sufficiently large markets, potential billion $ outcomes for a startup which takes the early mover lead. Two robotic hands that can work in co-ordination just as human hands do. Extremely difficult to solve, but money is there.
1. The cost & technical limitation. The cost, as some of the solution per problem OP suggest include "Lidar, visions and sensor" and all of those thing cost a lot by themselves. On top of that you need good actuators (Harmonic drives etc) for precision, and then good computing unit to handle all of it. Now you also need more power supply, and if it is mobile it needs a battery. Now your robot have a price tag only Arabic princes and well funded academic labs are interested in. And we haven't even touched the cost of try&fail iterative engineering process to make these work. In that process most companies/labs realizes the problem/condition have to be severely limited (run time, indoor/outdoor, general applicability vs made for one & one application only).
2. Human resource. Really, there's not much money in robotics, as a robotics engineer. Software robotics engineer can get a better working condition, security, salary & fulfillment in a software company. Mechanical, EE, embedded, etc is in a similar situation. Most robotics people I know are in for the passion. Application specific development (that is the norm right now) also require very niche knowledge that is hard to find.
The problem is of course until we can solve the problem of making it work at all price isn't a consideration. You can go bankrupt advancing the state of the art which then is enough for someone else to take your work and (repeat the bankruptcy part many times until someone works it out), and finally someone makes a ton of money with their useful robot.
You're right, but also software is weird. The world is absolutely littered with good computers that other people have already paid for, just waiting to be put to use for your project to expand their capabilities. If every new web app required its own little pocket computer to run, that you had to convince your customers to buy and keep in their home, it would be much less profitable to develop web apps.
The world is not littered with idle, high-performance robots waiting around for your motion planning algorithm to kick them into action. That makes it a lot more expensive and a lot less profitable.
You will find the most automated Mc Donalds in the world in Switzerland. Mc Donalds over there has a lot more automation there than it does in the US, both in the cooking and in the order taking.
Either this is because the automation is extremely difficult to do, but is simpler in Switzerland. Or alternatively, this is because in most countries in the world humans are cheaper than the automated system, even after it has already been developed.
As someone who does research on robotics for a living. The problem is not the former, but the latter.
For a consumer, I don't know if the equation 'human labor cost << robots' holds true. It is a hassle to get human labor and there is no scope for time arbitrage. A robot can do the dishwashing job at night for example. Unlike a traditional dishwasher, you don't have to load the utensils. Just leave the utensils in a sink and you are done.
Rethink Robotics, a Rod Brooks startup, tried that, with "Baxter". Company went bust.
There's good, simple commercial hardware for high-volume vegetable chopping and dishwashing, and it can be found in most large commercial kitchens.
There's a huge amount of special purpose machinery in the world. Most of it is pretty dumb. Newer machinery tends to have more sensors and a bit of self-adjustment. Vision systems have become parts of much industrial machinery - they're cheap now. Mostly they're looking for things aligning or looking like a known good object.
ABB's YuMi is perhaps a better example.
Unless real human hands continue to cost less.
If robotics and machine learning can progress to the point where household robotics or general-purpose robots become a thing, there will suddenly be an explosion in demand. Salaries for robotics experts will go through the roof, and all of a sudden, everyone will want to study robotics in school. This could take another 10-20 years to happen though!
Source: I work in an ADV company.
That said it's a problem that steers awfully close to needing a full real AI and that's been a showstopper for loads of potential solutions for decades now.
The ability to manipulate destandardized sizes would be useful but precision manufacturing ate most of the lunch long ago which reduces it to more of a "last mile" task.