/bin (and /sbin) were intended for programs that needed to be on a small / partition before the larger /usr, etc. partitions were mounted. These days, it mostly serves as a standard location for key programs like /bin/sh, although the original intent may still be relevant for e.g. installations on small embedded devices.

/sbin, as distinct from /bin, is for system management programs (not normally used by ordinary users) needed before /usr is mounted.

/usr/bin is for distribution-managed normal user programs.

/usr/sbin with the same relationship to /usr/bin as /sbin has to /bin.

/usr/local/bin is for normal user programs not managed by the distribution package manager, e.g. locally compiled packages. You should not install them into /usr/bin because future distribution upgrades may modify or delete them without warning.

/usr/local/sbin, as you can probably guess at this point, is to /usr/local/bin as /usr/sbin to /usr/bin.

In addition, there is also /opt which is for monolithic non-distribution packages, although before they were properly integrated various distributions put Gnome and KDE there. Generally you should reserve it for large, poorly behaved third party packages such as Oracle.

As far as deleting modem-manager goes, deleting the folder will probably only give you more problems if certain external programs are calling for it and its not there. I would find out what the underlying problem is for why it is giving you so many problems.