If I understand correctly, the restriction on magic item daily uses described in PHB1 is no longer the rules.
1) Is this true?
yes.
2) When did this change and where was it announced? Was it solely a bit of errata?
With Essentials. HotFL/FK, RC, and DMK use the new rules in which items have 'rarity,' only common items can be made/bought, and only uncommon or rare items have dailies.
3) Why wasn't it changed? I haven't used it, and it was a bit confusing to understand, but it seemed like an interesting exercise in resource management.
It was a nice mechanic to give a resource-management encintive to pressing on after a milestone. But, mainly, it prevented players from hording cheap lower-level items with Daily powers and using those dailies frequently. Since the new system put the acquisition of items with dailies in the hands of the DM, that was no longer a factor. Basically, a mechanical balance feature was dropped in favor of arbitrary DM fiat - not the only time Essentials did that sort of thing.
4) Does anyone still use the old rule? Why?
Yes, quite a lot of DMs, actually. Some because they liked the resource-management aspect of the original rule. Some because they rejected rarity, or Essentials in general. Most, though, just because there weren't enough rare or common items to go around, initially.
With the recent publication of the Mordenkainen's Magnificent Emporium providing a lot more rare items, I expect it'll be more broadly adopted.
So help me understand how this new "system" works. I have all the books in question. My understanding is that treasure parcels have been replaced by random treasure. I personally like the parcels and am using them. (Funny - since parcels were meant to replace the random treasure of 3ed).
Yes, Essentials went back to a random treasure system. On average, it gives out the same treasure as the parcel system. It does not replace the parcel system, which is still 'legal,' not that anything could stop anyone from using it. The random system /does/ reference rarity, so it's easier to use with rarity than the parcel system would be, but, really, the guidelines for rares are pretty strightforward: 1/tier/PC.
But I was unaware that there was actually a system involved with rarity. Or is it that informally you are allowed to buy common, buy uncommon with DM permission, and never buy rare? What more to it is there?
Nothing informal about it. You can only make/buy common items. Uncommon and Rare items are placed by DM fiat.
In my campaign, magic items can simply not be bought. Does that mean I am free to ignore the rarity system or is there something more to it?
The rarity system isn't entirely arbitrary. Uncommon items are more likely to have dailies or potent properties, and rare items are likely to have multiple dailies and properties, one or more of which may be intentionally overpowered in some sense. You need to keep rares /rare/, if, indeed, you feel the need to use them at all. If you don't want to use rarity to limit what items can be made/bought, you'll want to keep using the Item Daily limitation from the PH1.