In the past private light rail WAS built into open spaces. The classic example is in Southern California where entire cities grew up around private rail transit.
No, in the 90s and the 21st Century rail transit and highway construction are built to differing standards. In Colorado, for example, CDOT rules. If any proposal is made to share ROW etc., with CDOT, one can expect to having work around what CDOT is going to do anyway (Those of you that have attended CDOT meetings over the years likely remember the noise and anger, and, also how years later the highway link was built as presented at the meetings, anyway.)
This can be seen on the Trex line, which, had the public transit element been more powerful, would have not had to follow such steep grades and nor have had to built such tight curvatures in response to I25 Interchanges (this is true on all I25 interchanges except for I25/University and I25 at I/225).
This, too, is visible on the Taj Mahal line, where the segment from Simms west has the grade and curvature of a pretty good roller coaster.
CDOT is just a far more power political entity than RTD.
I presume that State Department of Transportation authorities, Nationwide, are more powerful than their public transporation counterparts, also.
Most other nations have nothing comparable to the huge and powerful state highway organizations that 'blossomed'

during the Interstate highway boom. Instead, I suspect, in most other nations, the organizations that handle transportaiton have handled capital construction of all kinds for many decades- which gives such organizations the flexibility to implement new transportation strategies.