the point of fridrich's normal f2l is to pair up slots of corner-edge pairs while preserving a cross and slotted pairs. this can be done completely intuitively with no algs.
the point of "your" method is to pair up corners while making the cross. this is a step backwards from the most popular form of f2l.
a major step in f2l is to make the cross in as few moves or as quickly as possible. this method doesn't teach that at all, and in fact does not allow the user to practice making a cross at all. if a user was proficient at making a cross quickly, s/he will probably regress by using this method.
pairing up first layer cross and corner pieces is nothing like pairing up f2l pieces. in f2l, you should be preserving the cross as well as any slots that you've already completed. this method doesn't teach this at all.