You do NOT want to install anything to which you need write access in your c:\Program Files\ or c:\Program Files (X86)\ directories.
Afaik a write only install is fully supported. (it works on Linux, and should on Win too)
The problem is the mentioned "tools" => Lazarus and Fpc sometime use tools from the GNU collection. Like: make, windres, gdb ....
Especially windres can not always be avoided (afaik, it will/may/can be replaced by fpcres, as soon as that will be released)
Some of those tools fail, if they need to be given a filename that includes a space. While on Linux those spaces can be escaped, afaik on Windows they can not (or no one has figured out how).
That is why the installer, does not want spaces...
Yet, that may actually not be a requirement for the install dir. It may possible be more an issue with where you save your projects. But I have not recently tested this.
And I guess no one else has. So potentially this "no space" issue is (at least partly) an artefact, or maybe not.