In the legal sense you are correct. Realistically, the seller can include chattel in the price he asks for the real estate/property as long as it is not identified as such. I seriously doubt these items would affect the appraisal unless they are gold plated or the property in incredibly cheap.
If it were included on a contract the lender would specifically ask the appraiser to comment on whether it was given any value and if so it would be deducted from the appraised value (and of course no competent appraiser is going to say he included chattel in an appraised value of real property)
Also, I know my transaction (I knew the seller) and purchased the property at less than market value (slightly -based on the current comps at that time) and the seller also gave me a credit to replace the carpets so I'm pretty sure the old washer and dryer in the garage (worth maybe $300 at that time which was 13 years ago) were not imputed into my purchase price
They also damn sure weren't part of my mortgage so your premise that I "likely ended up paying much more for that used washer and dryer then it would have cost you for fancy new equipment" is total nonsense