I believe this is not an ideal thing to do but I'm wondering all the reasons why (if there are any beyond what I can think of). I was having an argument with someone who insisted that shooting everything at 50 FPS for a production that would include some 50% slow motion speed and some normal motion speeds was the ideal way to do it and 50 FPS converted to 25 FPS would produce identical results and make no difference.

What I can think of off the top of my head is:

1.) You would be forced to use higher shutter speeds which may not be desirable. (1/25 vs 1/50 if ignoring the 180 rule or 1/50 vs 1/100 respectively).

2.) Regardless of shutter speed would you not end up with choppier looking video? The way I imagine it in my head is if you have 50 fps footage which you want to display at 25 fps at normal motion speed you're going to have to drop half the frames. If you drop half the frames then you are dropping half of the motion that was captured. I'm sure there are software techniques to deal with this and smooth it out but just like it's not ideal to shoot what should be 50 FPS slow motion at 25 frames and use software to convert to 50 FPS I'm sure this isn't ideal and has various drawbacks - right?

Are there any other reasons?

Shooting at 50fps to be played back at 25fps - (just cutting frames - with no slow mo) - your editing software should be able to do that with no issues as it's just removing every second frame.

I would if possible, shoot the stuff that is not going to be slowed down with the shutter speed at 1/50 so it would look fine (normal?) when played back at 25fps - though if you don't know what will and will not be slowed down in post, (which i would assume is the case or you would just shoot it at the 2 different speeds), I would run some tests with it and try and find a shutter speed that will work (though not ideally) for both the over-cranked and normal.

I would personally ask for some better pre-production and decide before shooting what will and will not need to be over-cranked on the day.

One of my cameras shoots 1080p50, and I just leave it on that setting most of the time. My NLE automatically converts it in real time to match my project setting (which is usually 1080p25). Then if I want slow motion, I can just adjust the playback speed accordingly.

I've never noticed any "choppiness", or any other undesirable effects. In fact I think it's a lot smoother than standard 25fps video.