It's not really a matter of it being shot in film, but rather how your typical TV works.
This video gives you a bit of an explanation of why NTSC runs at ~30 fps (PAL is 25 fps in comparison). While this is for NA NTSC, this is still applicable generally to Japanese televisions.
In the age where analog TV is deprecated (just just removes certain technical barriers, allows for more bandwidth), the frame rate used in analog video systems are still used and incorporated into DTV and HDTV standards. For the interlaced 1080i format, each frame is composed of two fields, each displayed every 60th of a second with a complete frame displayed every 30th of a second, using an NTSC ~30 fps frame rate. Alternatively, with the progressive scan format (720p/1080p) it is displayed twice every 30th of a second.
Television programming (at least with the NTSC standard) is broadcast at 30 fps (actually 29.97 fps), because traditionally television sets were 60 Hz, and would display 30 fps in an interlaced format, which mean the in one cycle, these sets would draw half of the lines of the picture, then they would interlace the missing lines. Therefore 60 Hz divided by 2 cycles per frame equals ~30 fps.
Playing film content (24 fps) has some quirks on a standard 60Hz TV, after all how would you do about dividing the 24 frames into the 60Hz? The TV industry this thing called a 3:2 pulldown that essentially would use 3 cycles for one frame and two for the subsequent frame. This is done to shoehorn 24 frames into 60 slots and produces some unnatural jitter that usually goes unnoticed to the untrained eye.
Anime, in general, is done at 24 fps and 3:2 pulldown-ed to 30 fps. Actually doing animation at 24 drawings per second, is very costly and generally inefficient. Most High quality animation is animated at 12 fps/8 fps (depending on if it's in the foreground or background) or by 2's/3's. This means there are 12 (or 8) drawings per second, each held for 2 (or 3) frames to make 24 fps. Anime takes shortcut for labor and budgetary reason and most foreground scenes are animated by 3's/4's (sometimes 2's depending on the amount of action). CGI anime on the other hand is a whole other beast and best left for another topic for another time.
Much of the 30 fps movies you see are telecined and made from a 24 fps master (i.e. not typically shot at 30 fps). So out of 15 frames (of 30) you'll notice that for every 5 frames, there are 2 frames that are interlaced.
The 24 fps standard was the smallest number that was easily divisible by 2, 3, 4, 6, and 8, which allowed editors to quickly find where to make their cuts which proved to be very cost effective production wise.
There are rare instances where animation is comes in 1's but it's rare. Bubblegum Crisis 2040's opening sequence consisted of some shots that were sped up to 29.97 fps. But the animators were not trained to animate at that fps, so it came out very weird with some parts being a little bit too fast while others being too smooth for a typical anime of it's time. During the pre-HD era, anime was shot at 24 fps and then interlaced to 29.97 fps and then blended with 3D CG at 30 fps, which looked fine on older TVs of it's time but come out looking pretty rough when converted to more modern and progressive formats, esp for blue ray
A notable example is in Disney's opening segment of Disney's Beauty and the Beast, where Belle gets on the wagon. These are high budget productions of with your average anime budget pales in comparison. In the past, anime was shot on 16mm film and was of comparatively lower resolutions compared to Western counterparts.
Early animators and filmmakers figured out to create the perception of motion through much trial and error. What they found was that somewhere between 12-16 fps would do the trick. If you fall below that threshold your brain just percieve it as a series of images displayed one after another. If you go above it, you get moving pictures.
As post people know these that while this illusion of motion works at ~16 fps, more frames makes for better (i.e. smoother) quality. Thomas Edison found what he believed was optimal frame rate 46 fps. According to him, anything lower than that resulted in discomfort and eventual exhaustion in audience. Which led Edison to build a camera and film projection system that operated at at a high frame rate.
The slowness of film stocks and high cost of film (35mm was the norm) made this not a good standard or starting point. It was more shooting closer to the threshold of the illusion of moving pictures as most silent films at the time were filmed around 16-18 fps and then projected closer to 20-24 fps. This is the reason while old silent films seem sped up, sometimes used for comical depicts like with Charlie Chapman.