It isn't just CARBON steel that makes taps and dies from them undesirable. It's that there are different grades of carbon steel,and the Asian ones are very likely made of the CHEAPEST grade of carbon steel.
I have hundreds of good,old USA taps,many of which are carbon steel,and they are fine. Not as durable as HSS. Carbon taps used to be recommended by some professionals because if you break one off,they are easier to get out. You can heat the part to remove their temper,use alum to dissolve them,etc.. Break off a HSS tap,and you'd better have a milling machine with carbide end mills to eat them out(which is what I most often do). I was always milling out broken off taps for other craftsmen when I was Master Toolmaker in Colonial Williamsburg.
Carbon steel comes in several varieties: Starting with 1050,which means there is .050% carbon in it,just BARELY enough to harden,but POOR durability and edge retention. Then,there is 1070,1080,and the best is 1095,with .95% carbon. And who knows what cheap crud the Chinese make up for their own products. Good,old USA taps and dies in carbon steel will be the 1095 variety.
That said,I do prefer the HSS taps,because they do last longer,and I have the means to mill them out. I also have a set of those "tap extractors",with the little fingers that stick down,and slide into the flutes of broken off taps. I got them to work ONCE. Whether you can mechanically extract a broken off tap depends upon WHAT odd chip of metal,or broken piece of tap,which you cannot see,is jamming the tap in the hole. Often those little bits of metal are beyond the strength of the tap extractor's fingers,and you'll break off the extractor's fingers trying to get the tap to turn.
That sharp,little "POP" you hear when you reverse a tap in a hole,is because the little tips of the taps are pressure welding themselves into the hole. That pressure weld can be too much to mechanically remove the broken tap.
Then,there is the problem that taps come in 2,3,and 4 flute configurations in the smaller sizes,at least. You need to have an extractor that matches the tap. You need quite a few of those things to meet all possibilities.
If you are REAL lucky,you might come across one of those little EDM machines that eat away taps. I could have gotten one once,but it took up a 2' square of space,and I am too crowded to devote that much space to the infrequent removal of taps. I just mill them out anyway.