The popcorn is sprayed on, often directly onto the drywall with no primer underneath. Scraping it off will tear into the paper, and you'll have lots of uneven spots, gouges, etc.
Also, nail heads aren't treated as carefully, because they don't show thru the popcorn, but are extremely visible on a flat ceiling. If the original construction didn't use enough nails, you may have gaps between the sheets, nail pops, etc.
I have had a flat ceiling, and LOVE the look, so I understand your desire. If I had to to it myself, I would have a professional remove the old ceiling and replace it with fresh board (have them use the heavier board and nail the heck out of it, so it doesn't sag), tape, sand, and paint.
This is a good opportunity to run speaker, phone, internet, power lines that upgrade the house, too. Add insulation for soundproofing, too.
I wouldn't have them try to mount fresh board over the popcorned surface, since you'll never get the board edges to match up well, and getting smooth seams is critical in that ceiling. It'd be harder to find the studs, the additional weight could cause the rafters to sag, all that is a concern.