It would be a very unbalanced idea
A lot of classes are fairly front-loaded in their abilities. Often the first three levels of a class are already very good for multiclassing, which is why you see people "taking a dip" in a few levels of a class. After that, they get very few, if any, interesting things in their subclass.
Let's, for example, start multiclassing into Druid!
I'm a level 14 Druid of the Land. I'm not going to get any new features from that branch of subclass anyway, so now I'm going to take 6 levels in Circle of the Moon druid instead, and all of a sudden this exact same level 20 druid build, under your new rules, loses absolutely nothing (or level 8 and 9 spells, depending on how you rule spellcasting progression), but gains far better wildshaping.
This is just one example, but there are plenty of classes where being able to 'dip' in a different subclass of the exact same class will result in not losing anything, but gaining extra powers.
It penalizes players who don't want to start figuring out how best to multiclass in their own class to min-max their character.
It's confusing as heck
A lot of class abilities just say "Druid levels" or "Fighter levels". RAW reading, multiclassing into your own class will allow you to stack those abilities. This change is going to be extremely confusing to figure out. Both my versions of the druid have Wildshape, do the levels of those two druids stack together? Can I only turn into non-flying creatures if I pick a CR above 1 because I'm not high enough Circle of the Moon to fly, and my Circle of the Land won't allow me to pick above CR 1?
Depending on how you start RAW reading, a lot of classes get unfair benefits by multiclassing into themselves, while others do not.