Why isn't .profile sourced when opening a terminal?

1. Because terminals don't usually run login shells by default. They also usually have options to run login shells, which do source .profile.
2. To control the behaviour of login shells.
3. Depends on the shell. For bash, see the set of startup files.
4. Not in some sense (updating login records, for example).
5. If you have a folder called bin in $HOME, the default .profile for Ubuntu does add it to your PATH. Since .profile is sourced at login (even with a GUI login), it should be part of your PATH for non-login shells started after a re-login. It isn't wrong if a directory appears twice in PATH, see this U&L question for details.

I found I had to edit the Default profile. In the terminal, click Preferences > Profiles > Edit > Command > Run command as login shell

Afterwards new terminals would source .profile script.