put simply:
dangerous, perhaps, but only to -your- user account. it's not shared with
any of the other user accounts you may have on the system.
 
stuff installed as root usually means software installed for all user accounts
on the system. shared applications.
 
if your user account does not have any special privileges, then software
installed by and running as your user id is not very dangerous.
 

The key thing isn't **what** you are installing, but **where** you are installing it to. Limewire can be installed anywhere - it doesn't require any files to be written to /usr, or to any other directories requiring root access. The install is really just an unjar, so root privileges aren't necessary.

Its actually no problem at all. If you do not enter root access, you will realize that Limewire cannot be installed into any other directory than your Home directory as it is with all other software. You can trash your Home directory any way you like. No security issue there. A harmful software can only cause serious damage if it's installed using root access and thus have access to all impt system files. So actually its more secure to install software without using root access.

So if it is "safe" what about my second question, if this type of installation only effects the home directory, which in my case (and i'm sure many others) is the only user directory on this desktop, why dont all applications install as simple binaries, or at least have that option?

flippantly: because you're running a multi-user operating system.
 
seriously though, many applications are designed to store configuration data
and user files in a user's part of the filesystem while the application binaries
and libraries are stored in the system's part of the filesystem for reasons of sharing
and protecting the application itself from the actions of users.
 
this separation of user config+data from app bin+libs is also reflected in the filesystem
layout and usage accounting in that the /usr/bin directory often lives on a partition
or disk separate from /home.
 
Similarly, the system backup strategy is positively affected since the infrequently changing
and possibly quite large collection app bin+libs files need backing up less often
than the frequently changing and often relatively small collection of user config+data files.

Quite true. GNU/Linux is a multi-user system. Many software if not all, allow you to install in your home directory without root access. But this will result in other users on the system not being able to access that software.