There has been no effective border between the UK and Ireland since partition in 1921 (bar some border checks during “The Troubles”). To suggest, therefore that, as part of Brexit, the UK should consider “regaining” control of a border which has never properly existed is somewhat stretching credulity. Ireland is not part of Schengen and has (roughly) the same measures in place to prevent illegal immigration as has the UK (except that, being a little farther away from mainland Europe they are less prone to invasion). There is no reason to believe that this will change post-Brexit. Of course if illegal migration to Ireland from the UK (or vice-versa) should become a problem then the matter will have to be revisited. Personally I don't think there will be such problems and the borders the UK seeks to regain control of are those that existed before 1973, not one that never existed. There are far more important things to sort out in the meantime.