The perspective will be the same with a 24mm or 200mm (or any focal length) as long as you stay in the same position relative to the subject, if you crop in the 24mm to get the 200mm field of view you'll get the same image with a much lower resolution and much wider depth of field (ie blurred background)
The perspective distortion happens if you physically move closer to your subject to get the same framing on the 24 as you had on the 200
It's not usually a concern until you get to <20mm, and especially not if you're going to crop the center of the picture to mimic a 50mm perspective.
I agree that, in general, wide angle lenses are harder to design in term of distortion control, but it's not a god given rule that all lenses wider than 50mm have to show distortion
Here is a 28mm with virtually no distortion: https://www.lenstip.com/233.6-Lens_review-Leica_Summicron-M_...
Here is the same with a 35mm: https://www.lenstip.com/610.6-Lens_review-Voigtlander_Apo_La...
Here is a 50mm that shows as much distortion as the two I mentioned before: https://www.lenstip.com/205.6-Lens_review-Leica_Summicron-M_...
If you’re talking about wide angle ‘distortion’, then on an iPhone (with the default settings) that’s just what a rectilinear projection looks like with a wide field of view. Zooming in digitally ‘corrects’ that just as much as using a longer focal length would.
You can easily confirm this by taking side by side comparisons. There are many of these you can find by googling, as this is a popular myth. E.g. https://www.photoreview.com.au/tips/shooting/perspective-and....