The downtime is not generally a requirement for subclass abilities. While I get your position there is no downtime for example when a figther goes to 3rd level, selects Cavalier and chooses proficiency in History. He just gets that skill immediately without any training, so why wouldn't someone who changed to Cavalier at 7th level also get it without training?
Because it is assumed for levels 1 and 2 he has been developing the abilities he gains when he obtains 3rd level and becomes a Cavalier.
For subclasses at 1st level, that training is part of their development for the class.
If you allow a "subclass-switch" when a new subclass feature is obtained, you have a few levels since your last one and, again, the development can be assumed during the downtime, etc. between those levels.
For example, our Cavalier at level 3 choose, at level 7, to gain the first features of a Champion (3rd level) instead of the Cavalier features (7th level). He has 3 levels in between to develop the features, whether they are Champion 3rd or Champion 7th.
Now, with Tasha's, being able to "unlearn" your prior subclass features and obtain multiple levels worth of features for a new subclass without making it via some downtime seems less plausible to me and stinks of gamism.
I get the in-story part, but the player is writing the story so it is up to them to come up with that - "I was visited in my sleep at the inn by the Avatar of Hekaton and he instilled the power of the Giants in me (RK new subclass) .... The dream also seems to have damaged my brain and I have lost the ability to cast spells (EK old subclass). Now let's get on the road to the Gnoll's lair."
For some instances, maybe, but for many stuff like that doesn't quite fly for me anyway.
I think switching subclasses is generally easier in story than multiclassing into a Warlock mid-campaign. That is the only one I have had trouble with in my campaigns.
I'm not a huge fan of multiclassing because of such things. What I don't mind is the older versions of multiclassing where you have to keep the levels close.
Then it makes since that the PC has been "training" in both classes prior to adventuring, from the beginning, and continues to develop both.
Multiclass "dipping" is a horrid thing IME.