We've done it several times. You do 'lose' some time on the transfer day, no doubt about it, but there are several good reasons to do it.
It's nice to see two resorts. The change in dining, location, and pool themes are fun pluses.
It can be a money saver. Usually, I book the resort before my flight. Sometimes it's a bit less expensive to fly out a day early or stay an extra day, but maybe a room at our main resort isn't available. Perhaps you can get a room for one night at a value resort. Recently I something else happen - the airline called to suggest I go a day early to avoid a major storm. So an inexpensive option was in order.
You can also do the opposite, spend that last night at a higher end resort than the rest of the trip and spend the day relaxing.
Another time split stays are very worth doing is if you want to see the other Olrando. WDW is a bit of a drive from most of the other Orlando attractions. It makes sense to stay closer for less money, or to stay at one of Universal's resort for the benefit of FotLA.
One last thought - it pays to pack smartly. Don't unpack everything at the first resort. Pack a day bag - or a two day bag. Conversely, when switching resorts - put all your dirty stuff in one suitcase. If you'll have a car, you may be able to leave the dirty clothes in the trunk. Just don't leave any food stuffs, make-up, or perishables in the trunk of a HOT car! I usually put all toiletries in Ziplock bags. It makes things easy.
IF going between two Disney resorts - DIsney will transfer your luggage for free. However, if yo have a 'package deal' at the second resort - you will need to check-in there to get your park tickes and meal credits. IT may make sense to use a taxi ofr that. Also, if you have DIsney transfer your luggage, it won't arrive until after 3pm. The new room may not be ready until then anyhow. If you transfer luggage yourself, Disney can hold your luggage in bell services. That way it willbe kept in a secure area with AC, not a hot car.