A few further thoughts along this line:
re: ” he expects his disciples to do the same thing “
In the extended Supper Discourse of the 4th Gospel, Jesus says a great deal about the coming of the Spirit among the disciples, but it seems to me that he doesn’t promise that they will be “empowered to heal” by the Spirit.
Rather, what he says is that they will ask the Father “in Jesus’ name” and the Father will do for them whatever they ask. Further, he expects that the disciples (at least those present in his hearing, the apostles and perhaps a few others, including the “beloved disciple” – who I take to be Lazarus, following WItherington’s argument) will do more signs than Jesus himself had done.
It seems to me that the point of view of the author of the 4th Gospel (or at least of his source(s) for these stories) is that Jesus healed through prayer to the Father and the apostles would do that themselves after Jesus’ departure, since the Father would do for them whatever they asked in Jesus’ name. The Father had “always heard” Jesus up to this point; in the future the Father would “hear” the apostles, too. (Perhaps this underlies what seems to me the implication in Jn 16:23 that the apostles up to that point had come to Jesus with their requests to “get things done” ; their own prayers up to that point were not reliably granted but would be in future, when asked “in Jesus’ name”)
Perhaps it is reading too much into the famous statement in Jn 20:21 to see significant analogies between the sentness of Jesus by the Father and the sentness of the apostles by Jesus, but I am tempted to see “healing through prayer to the Father” as one of them.