Gillette's Mach 3 cartridges were a big leap forward in blade manufacturing technology. Of course, they were accompanied by a slick marketing campaign that helped propel them to a financial success for Gillette. Since shaving is a very personal thing, there's plenty of room for different opinions on what's best. I happen to think Mach 3 is an excellent, albeit expensive, product.
For sure though the main reason for the multi blade razors to exist is just profits. The double edge safety razors were extremely good at what they did and all made from brass. Design from the turn of the century and perfected through the 20's up to the 60's. They practically don't ever fail. Towards the late 60's Gilette had issues and had a brilliant idea to increase profits. That is how the disposable razor was invented. First a two blade, then three...
8-10$ gets you a pack of 100 DE blades from a bunch of manufacturers on Amazon (depending on how much you shave, most typically do 3 or 4 shaves per razor so this is enough for years if you only shave every second or third day).
Cheapest Mach 3 I found on Amazon is 1,99$ per "cartridge", when you buy 15 of them for 30$. Otherwise they're generally around 2,5$ per piece. The even more fancy fusion proglide 5 blade Gilette cartridges are in the ~3,5$ range.
And add to that all the disposable plastic waste this produces. The DE razors are stamped and sharpened and generally wrapped in waxed paper. These cartridges have small razors moulded in plastic and then packaged in a bunch of plastic... I'm not the one to usually rave about the environment but I do appreciate the simplicity.
More relevant to this thread, the Merkur razors are made in Germany. I own a vintage Gilette Slim Adjustable from 1966 and a modern Rockwell 6S (splurged on this one, both are made in USA and the Rockwell is just made to a really high quality and works perfectly for me for 4 or 5 years now). Actually with the Rockwell I sometimes use the same DE blade for weeks just cause I'm too lazy to swap it out. It does not snag. Since buying it and a pack of 200 Astra blades, a brush and Italian Cella shaving cream (also crazy cheap for how good it works and lasts forever, think it was 10€) back then, I did not invest anything in shaving since. Still got more than half of those blades and the cella tube is half full.
Was worried I'm wasting money at the time and I'll end up not using it, but I'm glad it paid off.