It is not "semantically wrong": conceptually, you can compute a join by taking the Cartesian product and then applying the join predicates to the result, which is actually what the implicit join syntax suggests. Semantically, there is no difference between applying an (inner) join predicate and applying any other predicate. There is also no actual division between "building the set" and "filtering the result": different predicates might be applied in different orders, before or after different relations in the query have been accessed.

I started out writing joins in the where clause; i'm not sure why, probably because that's how it was done in the first book i read. I then worked with some old Oracle hands who also did it that way, probably because of tradition. A year or two ago, i rediscovered the explicit join notation, and switched over to it completely in a matter of days.

As you say, explicit joins are right because they separate which tables/which relationships and which rows. Those are not particularly distinct things in the pure relational algebra model, but they are fully distinct in practical use.