Warning! Star Trek Fan Theory
Jan. 24th, 2019 08:52 amI have read - though I was unable to confirm for this post - that when the transporter for the _Enterprise D_ was designed that they made the upper part resemble the platform of the transporter from the original series. It may even have used some of the parts, placed in the ceiling to prevent wear from walking on them.
Note that in _First Contact_ the Vulcans arrive by shuttlecraft, rather than transporting down. (The only transporting done in the movie was by folks from the future.)
So, here's the theory. At the time of _First Contact_ even the Vulcans didn't have transporters. That humans - going where Vulcans didn't have a reason to look - found a broken one in a derelict ship of unknown origin. They made repairs and through the decades some improvements, but were still feeling their way along.
Therefore, the reason they had so much trouble with the transporter in the original series was that they didn't have a full understanding of how it worked. That, in fact, every Federation transporter from that era had the beaming chamber installed *upside down*! :-)