You need tests and periods of isolation, with the periods of isolation being the more important component (that many people don't have much ability to choose right now).
What happens a lot is that people get tested, think they are safe, then after becoming infectious spend a bunch of time with people.
So advertising expanded testing isn't really a viable public health message.
I also expect that compliance wouldn't be all that high for at home testing (people skipping tests, deciding they still feel good enough, etc). It doesn't mean we shouldn't try to establish that access for people that would use it well though.
Also, there's a difference between working to increase testing so that more people do get tested before a holiday and making that the center of your message. They need to be careful to not mislead or give the impression that they are misleading, but they could limit the messaging to a statement about working to expand testing.