Now, I may well be mistaken about this one, not having been to Papal Masses for some time, but if my memory serves me rightly, from the time of Paul VI until recently, the procession has emerged from one of the doors in the façade of the basilica and sort of sidled to the altar. Here's a bit of a home video from YouTube which clearly shows Pope Benedict following the old Papal processional entrance from the Bronze doors, through the square, and thus approaching the altar from the front. Much better. Now all we need to do is to persuade him back into the sedia gestatoria.
Being a home video, please excuse the cries of 'is that hiyum?' and 'Oh my Gaaaaaaad!'