I'm sure that's true just from observing my washer as it's going through the "tub clean" cycle. All I added was bleach, but judging from the amount of suds that are churning around in there, there was a lot of soap residue.
As I mentioned in earlier threads on this topic, during the wash cycle you want to have just a few clumps of suds. Sudsing is not associated with cleaning. Suds do not form until there is an excess of detergent beyond what is needed.
If you are still seeing suds at the end of the rinse cycle, there is detergent remaining in the washer, which again means there has been an excess of detergent. Personally, I think that many of the detergent sensitive reactions that people have result from using too much detergent in the washer and could be solved by simply cutting back detergent to more appropriate levels.
Typically I use about one-tenth the amount of detergent recommended by the detergent manufacturer. For marketing purposes the amount of detergent to use that most detergent manufacturers recommend far exceeds what is needed. That's because they have to account for a person laundering an extremely dirty load of clothes. If the person does a load that overwhelms the detergent and the clothes come out dirty, that person will no longer use the detergent and that person will tell ten other people that Brand X detergent is vastly inferior to Brand Y (with Brand Y being a manufacturer who recommends excessive amounts of detergent.)
As with many things in life, find what works for you. Working with your typical laundry loads, start by cutting back your dosage by half. If the clothes still come out clean, cut it in half again. Repeat the process until clothes stop coming out clean, then go back to the amount of detergent you used on the last load that came out clean. Use that as your base and adjust up or down as appropriate loads that are heavier or lighter than your normal load.