To answer the question, none. As you said yourself, your lease specifies that the late charge is not a grace period.
Assuming that the "three days later" was after the 3rd, then it sounds like he has done everything in accordance with the lease. Your choices now are to pay your rent plus late fees, move out, or go directly to your landlord and try to work something out.
As far as does it make sense, that depends entirely on the market. If you're in an area with a weak market, then it makes no sense at all for him to do that. Late rent is better than no rent. However, he may have a waiting list for your space, in which case he may well be better off to evict you and rent to someone else.
Aug 9, 2013