Nobody's trying to make companies share their current patents, nor take away their patent rights.
At the same time, the public has a overarching common sense interest in making sure that any company that buys up patents critical to the entire telecommunication industry, will continue to license them for a reasonable fee instead of exercising the right to withhold them from everyone else.
That's why the anti-trust regulators are interested.
Everything in bold is contradictory. Instead of maintaining the charade of private property, why not admit you consider it just to determine who gets to use what based on "need" as decreed via mob rule.
Imagine if Nokia exercised their rights and said, "Apple, we changed our minds. We don't just want GSM/WiFi license fees from you. We've decided to refuse to license our patents to you at all." Goodbye, iPhone.
Notice that you said that nobody is trying to take away patent rights, but here you start a fictional horror story that the regulators must stop from ever taking place by "imagine if Nokia exercised their rights".
If you can't exercise a right, it's just a fiction.
tl;dr -- Courts have ruled that if the intent of buying a large number of patents is to halt any competition in that field, it is a violation of antitrust laws.
Correct. In fact, according to the Sherman Anti-trust Act (1890):
If your prices are too high, you are guilty of monopoly or "intent to monopolize".
If your prices are too low, you are guilty of "unfair competition" or "restraint of trade".
If your prices are the same, you are guilty of "collusion" or "conspiracy".
Anti-trust is a farce.