The number of PEs in the US seems to be around 500,000 per NCEES. That represents way more than 1% of all "engineers" -- there are not 50 million "engineers" in the US, unless Subway has started calling their employees "Sandwich Engineers" now. What are you counting as an engineer, if not a PE? For this discussion, an engineer would be someone working in a profession where a PE license is available, matching their day-to-day work. You could say "what about software engineers?" but that will skew your numbers, because we don't know how many SEs would be licensed PEs if a licensing program was available (which is kinda what we're discussing here).
The question is: for those professions where a PE license is available, how many get it? This is a number that seems a bit hard to find, but the consensus seems to be around 20%. So you're off by a factor of 20x. Please don't just make up random stats, or you will be contributing to the misinformation in the world.
I also don't care about the numbers of an organization who has a conflict-of-interest in the matter. I teach graduate level engineering classes and I know for a fact that almost nobody in my classes goes for the PE license. That is representative enough for me over the years.
I've been to work social events where all the alcohol was provided by the company, but they still had to hire a bartender. You'd pick up a drink, hand it to the bartender, and they'd open it and give it back to you. It sure seems like a stupid, wasteful ceremony; that is, until someone is on their way to getting blackout drunk and the bartender can start refusing to open more drinks for them. They can even use the line "I could lose my bartending license if I keep serving you." The requirement for a licensed bartender was not to make sure someone knew how to open the drinks, it was to make sure someone had the authority and accountability for keeping things under control. (Not to mention making sure everyone was over 21.)
Requiring a stamp from a licensed professional seems pointless up until it prevents a big problem. I'm not opposed to requiring that a Licensed Software Engineer (or whatever) sign off on the software running on chemotherapy machines, as long as that licensing is all done in good faith.