I do not myself believe in explicit Baptism of Desire, but I do acknowledge it to be an open question that has not been definitively settled by the Church's magisterium.
Both pro and anti BoD people have absolutely conflated the two issues, i.e. EENS and BoD. I have LONG argued that to both sides. What has happened, however, is that the anti-EENS people have redefined BoD into implicit BoD, i.e. the BoD of non-catechumens. Implicit BoD absolutely guts EENS and renders it a meaningless formula. Which is in fact why the anti-BoD folks have felt the need to attack BoD in order to salvage EENS. In order to do so, however, they have to attack St. Thomas Aquinas, St. Robert Bellarmine, St. Alphonsus, etc. In other words, by going after BoD in order to defends EENS, they're tacitly GRANTING the redefinition of BoD by the anti-EENS crowd and thereby inadvertantly making EENS much harder to defend. St. Thomas Aquinas, St. Robert Bellarmine, St. Alphonsus etc. only considered BoD in the context of catechumens. St. Robert Bellarmine asks the question: "Whether catechumens who die before receiving the sacrament of baptism can be saved?" There's no backing anywhere in the Church Fathers or Doctors of the Church for the implicit BoD of infidels. It's a complete novelty.