Firstly, I absolutely love what I am reading so far in 5E. I spent some time reading through the class section of the PHB last night and I am slightly worried (only slightly) that the specializations essentially force a character into a rigid framework. So for example, two clerics that choose to specialize in "Light" will be pretty similar apart from which spells they choose and their ability scores. It isn't a huge deal because there are plenty of specializations that you can choose and also with optional feats you can loosen up that framework a bit. However, it would be cool if some optional rules came out, maybe in the DM guide or an advanced player's guide, that allowed for universal specializations. Basically, this would allow you to choose class abilities from different specializations. So at 2nd level the character can choose any 2nd level class feature from any of the specializations. This should come at some sort of penalty to keep things balanced. What do you fine people think? Any ideas on how to house rule something like this? 
It would seem to me that allowing people to cherry pick specializations would be way too strong, especially if it was as generic as "choose one feature from any of these specializations". That will inevitably lead to broken combos of choices and people crying foul that the system is broken. I'm not even sure you could penalize it properly and keep it 'balanced'; the tipping point on the seesaw would be too violent. I think it'd be easier just to create More Specializations.
A universal specialization would be interesting, but I'd want to see the options presented therein to be limited and specifically chosen for the purposes of balance.
In order for your proposed system to work, each of the subclasses would need to be balanced at the same breakpoints, and their class features be balanced laterally. Alas, this is not the case.
Subclasses from different classes are not balanced against each other.
- For some classes, the lions share of their power comes from the subclass
- In other classes, the subclass accounts for a much smaller percentage of their overall power.
As such, being able to cherry pick your subclass abilities would allow someone to choose a class which is class-heavy, and a subclass which is subclass-heavy. Likewise, some players may unknowingly choose a class and subclass which is both class and subclass light, resulting in an underpowered character.
Furthermore, how would you go about balancing classes which grant subclass features at different points.
- The cleric gains domain features at 1st, 2nd, 6th, 8th, and 17th levels.
- The fighter gains archetype features at 3rd, 7th, 10th, 15th, and 18th levels.
- The rogue gains archetype features at 3rd, 9th, 13th, and 17th levels.
- and so on.
These features are balanced alongside what other classes gain at each level point, and are granted under the assumption of X-Class levels and all that entails (HP, proficiencies, skills, prior class features, level investment, etc). Being able to cherry pick say the 9th level rogue ability without any of its preceeding effects is potentially broken, due to the fact that said ability was balanced under the assumption of 9 rogue levels, each of which has reduced Hit Die, among other traits.
Finally, being able to choose subclasses from a different class would result in dead-levels. The 5E classes were designed so that characters gain something meaningful at each level, whether it be access to new spells, class features, ABIs/Feats, or subclass features.
You can do this sort of already. Feats basically grant class features. They are like multiclassing light.
I say if you want to house rule 'uniqueness' give everyone 1 free feat and there you have it. Your fighter can be a mage initiate. Your wizard can learn battle manuvers. Very fitting. ;)
Really, 'unwrapping' the subclasses isn't too drastic. It just goes from "here's what you get" to "pick one of these".
Doing so should probably be table-wide, because reasons.