Are there reasons to not use SCHEMABINDING on database objects?
I don't see any reasons of NOT using SCHEMABINDING on database objects. Its like safe guarding your objects.

Obviously there are pros and cons associated to it.

If you are not going to create Index Views, then you dont need SCHEMABINDING for views.

Basically, SCHEMABINDING 


prevents the views from becoming invalid due to the change in table structure e.g. dropping columns from table.
makes UDF's deterministic - as described at Improving query plans with the SCHEMABINDING option on T-SQL UDFs


The only downside that I see is, it will make changing the table schema a bit difficult, even if it is just a small change e.g changing a NOT NULL column to allow nulls.