The rectangle we have now is much more suited for human line of sight and was always how movies were shown. Was it technological limitations or something else?
The 4:3 aspect ratio (i.e., 1.33:1) of early television (and television up the introduction of widescreen 16:9) was chosen because it was a common movie aspect ratio. Very early movie formats were unstandardised. For example, the pioneering Roundhay Garden Scene (1888), perhaps the oldest surviving movie:
used a square (1:1) aspect ratio. However, 1.33:1 (4:3) was quickly converged on as the most common silent film format, based on the dimensions of standard 35mm film stock. What is often described as the oldest movie ever, Workers Leaving the Lumière Factory (1895):
Sound (i.e., "talkies") meant some changes. Since the audio was recorded optically on the same film as the images, just adding the audio track beside the frames would have pushed the aspect ratio towards square. The Academy of Motion Picture Arts and Sciences (i.e., the Oscars people) introduced a standard, "Academy ratio", in 1932, with aspect ratio of 1.375:1 (AKA 1.37:1). This was to be the dominant movie aspect ratio into the 1950s.
Thus, when the first broadcast TV standards were introduced, in 1936, there were two main movie aspect ratios in use: 1.33:1 and 1.375:1. They chose 1.33:1 (4:3). The next wave of TV formats were due to the switch to colour; the new formats were developed in the 1940s, introduced from 1941 through to 1951. This was still firmly in the era of 1.375:1 dominated movie screens. It is possible that if there had been a larger difference between the 1.33:1 of black-and-white television and the 1.375:1 of movies, perhaps more thought would have been given to switching TV from the old silent movie aspect ratio to the most common current movie aspect ratio.
The early 1950s saw a range of new widescreen formats coming into the theatres: Cinerama of 1952 with 2.59:1, Cinemascope of 1953 with 2.55:1 (changed to 2.35:1 in 1957) introduced by 20th Century Fox, and MGM, Paramount, and Universal using 1.75:1, 1.66:1, and 1.85:1 respectively, also in 1953. The most common widescreen format in more recent years is Panavision's 2.35:1 introduced in 1957 (and changed to 2.39:1 in 1970), but 1.66:1 and 1.85:1 are also common (but no longer considered "wide"). A key motivation for this switch to widescreen movies was the success of colour television - it was hurting movie theatre ticket sales. Widescreen let cinemas offer a visual experience that TV could not. The divergence between TV and movie aspect ratios was driven by the success of TV, and movies wanting to be bigger and better.
With a mix of movie aspect ratios out there, with new movies in widescreen ratios and old movies in 1.375:1, the widescreen TV format was chosen to be 16:9 (1.78:1), approximately the average of 1.33:1 and 2.35:1, and close to both 1.66:1 and 1.85:1. While clearly not ideal for either the old 1.375:1 format or widescreen formats, it allowed both to be displayed acceptably (expect for some purists who didn't find it an acceptable compromise), and the still-common 1.66:1 and 1.85:1 with little change, using either black bars or cropping.
More generally, we can note that standard paper aspect ratios were typically from about 1.2:1 to 1.6:1. 1.5:1 was (and still is) a common photographic aspect ratio. 1.33:1 falls solidly in this range (leaving aside the question of portrait vs landscape orientation). 16:9 doesn't push that far outside it.
There were many widescreen experiments in film before the 1950s. Lacking serious competition from television, none of them managed to gain enough usage to overcome the standard 1.33:1 or 1.375:1 formats. Perhaps most astounding among them was the ambitious Napoléon (1927), 5.5 hours at an aspect ratio of 4:1 (achieved by using three 35mm projectors side-by-side):
For comparison, some of the popular widescreen aspect ratios, all from 1953:
1.66:1 Shane: https://www.youtube.com/watch?v=4ddWyHhrIG0
1.85:1 Thunder Bay: https://www.youtube.com/watch?v=umKPXd7Pw0o
2.55:1 The Robe: https://www.youtube.com/watch?v=FN1gya6cqUc
The different common aspect ratios compared with each other: