An int is 4 bytes and a datetime is 8 bytes. The smaller your datatype, the more you can get on a page and the better use of indexes and RAM. But if you can get around with smalldatetime, this would also be only 4 bytes.
You probably could convert everything to numbers of days after e.g. 1/1/1900. In order to have an efficient search then, you would convert your search argument before selecting, so that it can make use of the index. But of course at least your display result would have to be converted with dateadd.
So in fact I don't see any real benefit using int. Using smalldatetime is in fact an additional constraint (only valid dates) and simpler.
Has anybody else seen other arguments?