Yeah, it's a bit hard to wrap your head around the logic (the mechanisms are not so difficult). It's kind of explained in this question:
http://www.cbafaq.com/salarycap.htm#Q26
I think the best way to look at it is that the league sees having cap room as an asset, and doesn't want to additionally reward teams that clear cap room with the ability to use their full MLEs and Bi-Annual exceptions.
Imagine a scenario where the MLE is $10M, the BAE is $4M, the cap is $120M, and a team has a salary coming into the offseason that has $106.1M worth of salaries. $106.1M + $10M + $4M = $120.1M, so the team is "over the cap" and can't sign a player to a contract without using an exception. They can use the MLE and get a player for $10M. But what if they want to get a player who will command almost $14M on the market? They can't combine the MLE and the BAE, but they can renounce the exceptions, and have $13.9M in cap space, and sign the player. Then, as a consolation for losing their full MLE, spending up to the cap creates the "room" exception, which is typically about half the size of the full MLE.
I kind of see the logic, especially for teams that clear out their entire salaries to try to sign two or more max deals. You want to be able to go out and dominate the the free agent market, spend up to the cap, AND get your MLE on top of that? The league says "no".
The cap is overly complicated, and there are tons of exceptions, and some of the logic is murky at best (the above is pretty murky). I'd certainly want to design a different system if I were given the opportunity to do so from scratch. But the whole thing is collectively bargained, and you've got to make the players happy, and you've got to make the small market teams happy, and you've got to make the big market teams happy to get everybody to sign on the dotted line, so you get what we have here.