Well let me take a shot. First off 55 Rc is too soft. 65 Rc is more like it. whats going on inside the steel with increasing carbon conttent? that is a good question. To consider it lets look at the phase diagram for steel, and consider for now only simple steels (carbon, iron, and minor impurities)
look at just the left side up to 2% carbon
steel can exist in many different phases depending on the temperature, and carbon content. These phases are ferrite, cementite (Iron carbide), pearlite, martensite, and some others but they are not directly relevant.
Ferrite is soft and relatively weak. Cementite is very hard and very brittle. Pearlite is a combination of cementite 12% and Ferrite 88% arranged in a layered structure.
When you heat treat your blade, Ideally all the pearlite becomes martensite which is tougher, and hard (~66 Rc). Martensite is what we want in our knives.
depending on how much carbon there is, the steel will be made up of one or more of these phases. If the steel has .8% carbon then after heat treatment the knife will contain only martensite, the good stuff. if the steel has less than .8% then you end up with martensite and ferrite which is weak (bad). if the steel has more than .8% C then you end up with martensite (good) and cementite. Extra Cementite is not bad because the cementite is supper hard, and contributes greatly to wear resistance.
so for knives and I would even say for most swords at least .7-.8% carbon is neccasary for a good end product. Swords can get away with a lower carbon content because nobody really cares about the wear resistance of swords. If you call it a sword then you indicate it will not be used. If you call it a large chopper then you expect it to be used, and so wear resistance is important.
I more complicated alloys the extra carbon will form carbides with tungsten, vanadium, chromium, molybdenum, and just about whatever else is present. This is usually very desirable because these carbides, like the iron carbide (cementite) are very hard and thus vastly increase the wear resistance.