Then you mean "depth of field" not "distorted perspective"

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

The thing is though that the depth is contracted disproportionally much more than width and height, which results in a non-linear transformation of perceived dimensions. This causes lines to bend. At 47mm straight lines aren’t bent no matter the distance from whatever there is in the picture. At shorter lengths there are always regions in your photo which are distorted in this way. You can’t fix that by changing your position. The only thing you’ll do is change what object is bent and in so doing maybe make it less obvious.

That's lens distortion, and has nothing to do with depth. Phones will correct it in software automatically, and Lightroom etc can also do it for your DSLR lenses.

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 have a 28mm lens with a symmetrical design that shows no distortion

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_...