Generally, the "limited" in third person limited is simply to distinguish it from third person omniscient, which is, by definition, unlimited.
As to your examples of the restrictions and repetitiousness of third-limited, a better way to show (instead of telling) what the non-POV character is thinking and feeling is through the character's actions. Sometimes you need to fall back on the POV character seeing anger in the other person's eyes, or some such quick-and-dull thing, but you also have the option of describing clenched fists and the like, which makes for a more compelling story than simply hopping into the second POV and writing "he felt angry." You don't need to be in his POV to write "he clenched his fists." (And, yeah, the clenched fist is a cliche, and I'm just offering it as an obvious example, but you'll want to come up with something stronger and more original.)
Switching POV from paragraph to paragraph (switching anywhere short of a scene break) is headhopping, and can be very jarring to readers, breaking the bond with the POV character, which is why it's not a good technique generally. Another consideration is that if you're telling the reader absolutely everything that every character is thinking and feeling, it can really kill the tension in the scene. Think about real life, and how not knowing for absolute sure what the other person in a conversation is thinking adds to the tension of the conversation.
I find it interesting that a LOT of writers feel the urge to headhop in sex scenes even when they don't in other types of scenes, and, really, sex scenes are no different from any other scene, in terms of writing. You've got two characters, each with slightly different goals, in some degree of conflict, and they interact until one of them achieves (or fails to achieve) his/her goal, and then the scene is over.
My personal theory -- and it's just a theory, nothing definitive, and probably doesn't apply to everyone, but I've noticed the tendency in myself and in some other writers I know well -- is that sex scenes are, for obvious reasons, highly emotional, and if you (the author) stay in one POV, you have to feel those emotions, and they can get a little scary, and when they get particularly scary, you (the author) can take a step back by switching to another POV instead of following the original emotion to its deepest and scariest conclusion.
The same thing is true in non-sexual scenes that are highly emotional; if the author gets scared by the emotions in the scenes, the author can be tempted to switch to another POV, instead of having to face the depth of the first POV's emotions. Which, of course, is bad for both the author and the reader, because it drains the story of the very emotion that a reader is seeking.
JD