It's not necessarily the silicon chips that they're talking about. Tantalum goes into capacitors, tin into solder, lithium into batteries. Neodymium goes into super-strong little magnets that hold the cover onto your iPad or the wall adapter onto your MacBook.
These various components were in many cases already made from more abundant elements in the past, but material science breakthroughs permitted great improvements that in some (relatively expensive) products were and are worth the extra material cost. Compare a Motorola "brick" cellphone from the 1980's to an iPhone and it's not just the chips that improved dramatically. Magnets can be made of iron, batteries can be made of lead, capacitors can be made of aluminum. It's just that those devices are dramatically larger, heavier or in some other way worse than their more modern counterparts.
Lately it's been getting questioned whether these are worth the human cost, the lives lost to war and slavery around the Congolese mines that source tantalum, tin, and tungsten. Another question is what will happen as China, which sources most of the world supply of rare earth elements such as neodymium, cuts back on exports to fuel its own manufacturing capacity. (Answer: Molycorp is reopening an old mine in California.)
It's a comparable argument to whether driving a car powered by oil is immoral when people are fighting wars for oil. The problem isn't so much that oil is rare today as that its clustered distribution over the planet makes concentrating wealth by monopolizing production easier than if it were distributed more evenly. Of course we can imagine supplies drying up within a few decades, but that's quite a bit further out than the 5-15 years most people will keep their next car. You can power a car with a coal-fired steam engine, or a coal-fired electric plant that charges batteries, or solar panels charging batteries, but gasoline has the best mix of features and price at the moment as far as most paying customers are concerned. It remains to be seen if the bulk of humanity will forego gasoline for electric cars before they cost less. Not many people are ditching their cellphone to go back to a rotary dial landline phone, full of copper and iron, even though it's cheaper.
It's not necessarily the case that things will inexorably get better. Batteries can be made from other elements that are orders of magnitude more plentiful, such as iron and sodium, but those batteries may not ever have the energy per weight of a lithium battery. It's possible that in a few centuries, after oil, coal, lithium, etc. are mined out, people will drive cars that have much less range than they do today, but that recharge quickly enough that it doesn't matter too much. On the other hand something much better may come along, or who knows, maybe we'll all be videoconferencing by then.
There are scientists working on these problems, but material science is a slow field. It's very difficult if not impossible to model the macroscopic properties of a new material in a computer. Progress essentially comes through educated trial and error. Even once a new material is fairly well understood, the theoretical model and experimental testing may not line up perfectly. Trying to concoct new materials from a wishlist of desired properties can take decades.