No there is normally no reason not to install as root, this is quite common. No "running" as root is not the same as installing as root. You should not run this as root, it is in my experience very seldom that an X client needs to be run as root.
Installing and running are different things. Many items need to be installed as root to get into the directories configured during compilation, but they will be run afterwards as "normal" users.
The installing is the final part of the compilation process. The compilation for many packages can be done as a normal user, e.g. in some subdirectory of your homedirectory. But when it comes to installing, the executable binaries and scripts to /usr/local/bin or /usr/bin, and other files to /usr/lib etc., you need the special rights root has to write there.¹
This is what you typical get with
tar xvf somepackage.tar
cd somepackage
./configure
make
sudo make install
Only the last command in that chain needs to be done "as root"²
After installation every user can use those executables, but, among other things, this prevents them from altering the "global" setup.
¹ There are more reasons to do this as root, e.g. when you need to set some setuid or setgid bits
² Often the last commands are chained with && so install is only tried when the make succeeded