Has the 16mm Apollo 11 [EVA] film always been available to the public?
Yes, but probably not in is entirety or as 16mm film, which was mostly for professional use or rich amateurs. Back in the 1970s we saw bits of it in movie theatres and on TV, and I believe it was sold in Standard 8mm and perhaps Super 8 movie format for home viewing.
Its important parts were included in the official 1969 movie, "Eagle Has Landed: The Flight of Apollo 11" No. HQa 181. According to an old video tape I have, that film was awarded: Certificate of Exhibition, Edinburgh Film Festival 1969; Certificate of Merit, American Science Film Association 1969; Gold Camera, US Industrial Film Festival 1970; Ionosphere Award, Atlanta International Film Festival 1970. Nowadays it can be bought on many DVDs, but all the ones I've seen are poor-quality copies from damaged and/or faded film.
Nasa's publication...
Data Users' Note, NSSDC 70-06, Apollo 11 Lunar Photography, April 1970...tells all about Apollo 11 photos and film - availability, cameras, films used, formats of available data, coverage and quality, summary of subject matter, and ordering procedures.
There's a bunch of scans of individual pages at the Apollo 11 Lunar Surface Journal
https://www.hq.nasa.gov/alsj/ under Background Material - Photography Reference (fifth from the bottom).
On page 6 it says:
16-mm Photography
The 16-mm sequence films are available as 16-mm positive or negative color film duplicates. For convenience, the individual 16-mm magazines have been spliced together and are available on two reels. It should be pointed out that this photography is suitable only for scientific investigation. These films normally will he provided on a 3-month loan basis, although in special instances arrangements can be made for permanent retention.
The EVA was filmed with three film speeds. Neil Armstrong at 12 and 24 frames per second, and shortly before Buzz Aldrin exited the Lunar Module he set the camera to one frame per second (page 3).
In the Appendix, it lists details of all 13 magazines of 16mm film, and on page A8 the EVA:
...
[Formatting edited for clarity]
Magazine J Frame Numbers 1-5612 This magazine is the initial sequence of photography from the LM on the lunar surface. It shows the start of extravehicular activity with Astronaut Armstrong going down the LM ladder onto the lunar surface.
Magazine K Frame Numbers 1-5610 This sequence shows activities on the lunar surface.
Magazine L Frame Numbers 1-1648 This sequence was taken from the LM on the lunar surface after EVA.
...
* Photography of intravehicular activity and of the earth has been edited from the 16-mm film magazines and is not available through NSSDC. This photography can be obtained from NASA's Public Information Division. (See page 8 for address.)
So there are 11,222 frames of EVA activity on 16mm film which were available in full for scientific research from April 1970, and portions of it were released for public viewing as soon as possible after the mission.