Chances are that an assault weapon will be used for offense rather than defense. You can't really CCW a rifle so you will probably be carrying a pistol if you are going to defend people while you CCW. Chances are that you will have a pistol nearby, and then have to go get your rifle if you are defending yourself in your home so you probably will use the pistol first to defend yourself. Its more likely that someone planning something or a criminal will try to use an assault weapon, so why not try to get as many of them off the streets as possible? I know that there's not a clear definition of assault weapon, but what do you really need anything that is non-pistol/hunting rifle for?
Well, firstly and foremostly because we don't have the Second Amendment so that we can shoot at deer or robbers. We have it so that we can shoot at government.
Secondly, the definition of "assault weapon" is aesthetic. It is whether or not the weapon
looks scary or militaristic to the person who happens to be writing the law. Actual military capabilities (for example, the M4 has a three round burst, the M249 is a fully automatic weapon) are already illegal for the general civilian populace unless you have a very special (and difficult to get) license from the ATF. So when the Administration says it wants to ban all "military style assault weapons", then it either means the ones that are already banned (in which case success! everyone goes home happy!), or it means the ones whose exteriors
look military, but which do not actually have those military capabilities.
Thirdly, it is actually (thankfully) less likely that a criminal will plan something with an "assault weapon", if by that you mean a rifle. As you point out, rifles are difficult to conceal about ones' person, meaning that particularly violent and/or organized groups carry them, but most criminals don't. Rifles are actually one of the least-popular murder weapons. Knives are used in five times as many murders, fists in twice as many. Focusing in on rifles in murder-prevention is sort of silly when all of these "assault knives" are lying around.
Fourthly, since rifles are unlikely to be carried out in public in a CCW manner, they are
more likely to be used for defense, rather than offense, since they are generally
staying in the home. Someone ripped out on meth in my kitchen at 2a.m. posing a direct threat to my children needs to be met with the biggest thing I can bring to bear, not the thing I can fit most easily into the small of my back.