Suds don't clean in and of themselves but are a byproduct of the
detergent.

The manufacturer of one HE detergent had this to say:

Can I use ARM & HAMMER Liquid Detergent HE in my regular washing
machine?

HE detergents are specially formulated to work best in HE machines.
While ARM & HAMMER Liquid Detergent HE will work (clean) in regular
machines, we recommend that consumers use one of our other liquid
detergent products in regular machines.

That's because the HE stuff will clean as well as just plain old
water. Water alone DOES clean fairly well. -Dave