Why use an intent lock at a higher level in the hierarchy, why not just a regular lock?
I think I have worked out the answer (Please correct this if my understanding is wrong)
After a bit more reading, I found a simple matrix here:

It appears that the X lock is less compatible with other locks than the the IX lock.
If we were to put an X lock on a table due to reading one row, we couldn't get an IS lock on that table but if we have an IX lock on the table we can get a IS lock.
If I understand correctly then, If we were to lock the table with an X lock to update one row, we couldn't read a different row because the read couldn't place an IS on the table. However, if we use an IX, it can get the IS lock it needs.
The following test seems to prove this is the case:
Update the single row:
USE AdventureWorks2016;

BEGIN TRAN;
UPDATE  Person.Person 
SET     LastName = 'Smith' 
WHERE   BusinessEntityID = 1;

in another session, SELECT a different row to the one being updated
SELECT * FROM Person.Person WHERE BusinessEntityID = 2

this row returns without being blocked
However, if I was to gain an X lock:
USE AdventureWorks2016;

BEGIN TRAN;
UPDATE  Person.Person WITH (TABLOCKX)
SET     LastName = 'Smith' 
WHERE   BusinessEntityID = 1;

this query is now blocked:
SELECT * FROM Person.Person WHERE BusinessEntityID = 2