Respectfully, I see this as a conclusion looking for evidence to support it. Nowhere does the text state that the gift of healing was
not used in either the case of Epaphroditus or that of Timothy.
What it does say is that Epaphroditus
was sick and almost died.
Nothing is said of his path to recovery. It is just as reasonable to conclude that Paul or another person laid hands on him and he recovered, as to conclude that Paul didn't, or tried and was unsuccessful.
As for Timothy, his malady was apparently minor, given that Paul advised "a little wine". Again, the text records
nothing at all regarding "attempts" at healing.
Paul's own malady was never healed. The man whose hankies had healed others was not healed himself. God's ways are higher than our ways, and we don't get to decide who gets healed and who doesn't. In the absence of clear evidence, let's not draw conclusions that happen to align with a particular agenda.