In the case of Liechtenstein every single one of the parties has an interest that the, yes, technically time restricted, status quo continues. Liechtenstein for its own reasons, the rest to reduce the exodus of too many wealthy families (there is absolutely no restriction on family reunification in Liechtenstein, one person moving into Liechtenstein then can get his whole family into there) into a low tax environment.
That interest wouldn't be there in the case of the UK. And yes, while they can invoke the Article 112 unilaterally, it has to be done in a restricted manner in terms of time of application and scope of application or the corresponding parties can of course similarly Article 112 against the UK.