Just to "correct" some of the misinformation here...
It is cheaper to ship the appliances than to buy new ones. We shipped a bunch of stuff air freight for about $2000 which included a washing machine, commercial espresso machine, vacuum (miele), books, dinner set, clothes, etc. It would have cost more just to replace the espresso machine than what I paid for the entire transport. That being said, I think it's a bad idea to try and relocate items like refrigerators and dishwashers - it's not worth the trouble. Our vacuum and espresso machine are both still working fine after almost 8 years being back, but the washing machine couldn't handle the different frequency. The drive motors and heating element worked fine, but the dosing system couldn't be adjusted to work on 60 Hz and misdosed pretty often. We got a new washer.
Some small appliances like cordless kettles would work here without any issues and would probably qualify as a heavy enough load to run a 240V recept to - while our kettles are limited to about 1500W (1800W is the most I've seen here) they typically run between 2000-2400W in Europe. The kettle we have here is also sold in Europe but our US model is 1500W while the EU version is 2200W - considerably faster at boiling water and more than 1440 volt-amperes. I don't think it would make economic sense to run a 240V circuit to a kettle (although I did so for one customer who had a very special teapot) but there are some appliances which the cost to replace would grossly outpace the cost of transport and running a dedicated line to and will work fine here like my espresso machine. Even the Miele vacuum was worth shipping, running a 240V outlet and making up extension cords for. Way cheaper than buying the same or similar vac here in the US.
US dryers, at least the older ones with mechanical timers, work fine in Europe. I had one for over ten years that I used to handle the laundry from my cafe. There was no equivalent beast available from an EU manufacturer unless you got into the outrageously expensive commercial units (which are three phase), so almost every family that came over as embassy staff had one and they sold like hot cakes at the embassy auctions.
I also don't know that I can agree with the theory that European ranges will have the neutral tied to the ground (or frame) internally. Almost every service in Europe is RCD protected and this would trip the main immediately.