Air carrier pilot reported a missed approach due to glideslope intercept on ILS 13L at JFK being located at a low altitude. Reporter suggested a notation about this aspect of the approach.

Narrative

After changing runways due to crosswinds at/exceeding CAT 2 limits; we used the 13L CAT 2. The clearance was direct KMCHI; cross BUZON at 2900 cleared ILS 13L. The intercept of the localizer is so close in that we completely missed the glideslope and missed the approach. On second attempt we studied the problem closer and VNAV'd to 1500 to capture the glideslope and all went fine. This approach is a bit odd and could use some kind of warning language to alert crews of the difficulty capturing the glideslope very close in and at a low altitude. We missed and the flight behind us missed; I am betting ATC is wondering why the high number of missed approaches? I spoke to a friend at a different airline to ask if this was a common problem; he said they are not authorized by their company to use that approach. I feel that we need to investigate this issue and warn crews about this unique approach.Cause: Unusual approach; that is doable but could use some 'heads up' notation about glideslope intercept at low altitude and close in; or something helpful.