Yeah, I understand what you're saying. It depends on the specific board we're talking about and there are so many out there that it's difficult not to generalize. There are very good value-oriented boards in each chipset and someone with general needs I don't think could necessarily go wrong with any of them. There are plenty of super-cheap boards out there that are still working just fine 7-8+ years later, so I can't see an H87 board (being of quite a bit higher quality than say an H81 board) dying far sooner than Z87 board. Many Z87 and H87 boards share much of the same components.
But again, I get what you're saying. If it's only a few dollars more and fits the budget, then why not. It's like when people suggest the Athlon X4 750K instead of the slightly faster and newer 760K. It's worth the extra $10.
You don't need an aftermarket CPU cooler. The stock Intel cooler works pretty good, especially if you're not overclocking.
The Asus Z87-A is a very nice board. 4 ram DIMM slots, supports crossfire and SLI and has plenty of other features. It's probably a bit more than what you need, but a very good board none-the-less.
It is a good idea, but you don't have to. The reason that a lot of people suggest this is because quality parts today are likely to either last a long time or be inoperable from the factory. If you put everything in a computer case and find out that something is not working, it becomes more of a hassle to work inside the case and figure out what is going on. Considering everything plugs into the motherboard, that would be the part with the most hassle if you encounter problems with it. If you find you received a bad MB (which happens with even the highest quality products) and everything is already installed in the case, you're going to have to take everything back out. So, yes, it is a good idea, but not required. Just be sure that you set your motherboard on the box that in came in or some other non-conductive surface. DON'T use an anti-static bag. Those keep your components safe by directing electrical flow around the outside of the bag, so the surface is basically conductive.