Would a table benefit if it was a heap
This started as a comment/questions but it got to long so I moved it here:

I'm really thrown by this question.  1.5mil rows isn't really all that big.  And the point behind an identity is that it's ever increasing.  If that's your CL you shouldn't be doing inserts into the middle of a page, certainly not often enough to cause the level of fragmentation you're seeing.

Couple of questions:

Are you doing IDENTIY_INSERTS?  Basically specifying what the identity value should be?  Or have you re-set the identity at some point so that you are inserting into the middle of the range?

Typically if you are doing inserts it looks like this:

5 6 7 8 &lt; Next insert goes here &gt;


But if you have something like this (assume your next identity value is 4)

 1 2 3 &lt; Next insert goes here &gt; 100 101  


Then you could be seeing quite a few page splits.  But in the normal course of things you shouldn't be.

Is there any chance you are shrinking your database?  Auto_shrink or a maint plan/job that does shrinks?  If so it's the shrink that's causing your fragmentation not the clustered index. 

In general there is nothing wrong with a HEAP and they can be faster for INSERTs.  My biggest concern with them tends to be if you are doing large numbers of deletes or updates (which you say you aren't).  In those cases you can get a space leak and end up with a table that is multiple GBs in size but has 0 rows.

Actual answer

Given you have a log file, and are only ever inserting, you could try dropping the PK and see how performance goes (in a test environment first of course). Once you've run some tests using your workload and seeing how things go then make your change in production and monitor there for a while. You might even consider dropping the identity column entirely. 

Do check that SHRINK thing though.  That's a killer.