As Launderess has pointed out in the past, natural soap has water softening abilities. The problem is that it tends to form a scummy precipitate as it takes hard water minerals up. So washing soda has traditionally been added to spare the soap, but the problem is that washing soda or sodium carbonate turns into calcium carbonate and magnesium carbonate, or limestone/dolomite, when it takes up hard water minerals. So unless you use a non-precipitating water softener, such as STPP or Zeolites, you get to choose between scum and cement buildup on your fabrics or washer internal parts.
Sudsing is just a sign of surfactant activity, although various surfactants produce varying levels/qualites of suds and foam. Surfactants basically are bipolar molecules that act to reduce surface tension, and that action is necessary to help break up oily/greasy soils from fabrics and hold them in suspension. But all you really need is a slight surplus of surfactant to do the job, and that is signalled by a light layer of suds in the wash water.
You may notice that often the suds start out low at the beginning of a wash, but increase as the wash cycle continues. That can be for several reasons, but I think the main reasons are slow dissolving detergent or soap, and the fact that the builder in the detergent or booster tends to saponify oily/greasy soils. Saponify means to turn into soap. So the action of the builder, which by itself produces no suds, with the oily soil, produces soap which in turn can produce suds. In any case, when I'm adding grated bar soap to the wash, I'll wait a few minutes to observe the suds level, before deciding whether the wash needs more. One nice feature of natural soap is that if over sudsing does occur, it tends to rinse away quicker than a synthetic surfactant does.
I still think that a properly formulated HE detergent is a good idea over using reduced amounts of a regular detergent. Most regular detergents are cut with sodium sulfate, which is merely a filler and has little cleaning ability on its own. Most regular detergents have high sudsing surfactants. This means you have to cut the amount way down to avoid over sudsing in an HE machine. In turn, that reduces the level of builder, anti-soil redeposition agent, enzymes, etc. to the point where they may be inadequate to achieve an acceptable level of cleaning.
A modern laundry detergent is a bit like a packaged cake mix. It has all the right ingredients allowed by law, but in fixed proportions. So if you need lower sudsing but still need maximum cleaning, you may be out of luck. Like a good chef, who prefers to make a cake from scratch using flour, eggs, milk, sugar, baking powder, etc., I prefer to add the surfactant (soap) separately from the builder/break/antisoilredepositionagent/waterwatersoftener (STPP). I can vary the amounts and proportions better to suit the type of laundry load and wash program.