super-type subtype discriminator in Primary key and design simplicty?

Referencing this great answer by PerformanceDBA:

The referenced answer approaches the problem of supertype subtype by :

1. using a Discriminator in the base-type ( which could be constrained by using FK and lookup table for TYPE)

2. creating a simple FUNCTION to check exclusivity which gets called using CHECK constraint in the subtype.

My question : if the discriminator is part of the primary key of the base-type and a User Defined Function is USED to check for exclusivity , would a design like this break any relational design or would it make the design simpler ( given that the PK is not multi valued of course) ?

Here is an example for illustration:

can call a function that checks for the ID of product and insert this into the desired table ( Jet table , Boat Table or Car table ) based on the ID?

if that is the case , can I get rid of the Discriminator column and the look up table too ?

is there any shortcoming of this approach ?

UPDATE to illustrate the two design approaches :

is there any shortcoming of this approach ?

Yes.

You have broken 1NF:

First Normal Form
Each domain (column) must be Atomic, that is, indivisible
with regard to the SQL Platform (Datatypes).

Your ProductID is a conglomeration thing that is made up from two atomic things:
    ProductType CHAR(1) -- {C, B, J, ...}
and some number within that, say
    ProductNo INT.

At the point of your table (which is not described) in the data hierarchy, the PK is an ordinary Relational composite key:
    ( ProductType, ProductNo ).
not:
    ProductID.

Now you don't need a Subtype cluster in that table.  

But I suspect you need exclusivity pivoting on some other concept: if so, you need to post a model of all the tables related to this issue.