Tanemon - Great question. The short answer: yes, everything is speeding up - healing, attracting, relationships, you name it.
The longer answer: Everyone comes across what Gay and Katy Hendricks call "upper limits" - self-imposed ceilings on whatever we want (i.e. healing, money, relationships, etc). Depending on our background and the amount of conflict we hold onto, this colors our perception of reality.
Many times instantaneous healers will employ techniques to satisfy the minds of their client's - not that it is actually needed. If someone feels that spitting on dirt to create mud and rubbing it on your eyes can heal you, then they will look for someone to validate their perception, or rather their "ceiling" on spontaneous healing (i.e. "I can only be healed if ____"). When in essence, the healing technique barely matters as much as reflecting an image of wholeness back to the person and letting them decide if they want to embody that and heal now.
There were plenty of times when Jeshua would heal someone, and then after he left the area, the person would revert back to their old malady - because their belief was that the healing was coming only from a master/healer, not a permanent condition. There were other people that kept their diseases (i.e. blindness, leprosy, etc) because they were not finished playing with that particular experience.
And yet on the higher levels of consciousness, we can even heal others even beyond their desires. The example was when the blind man said "No don't heal me! I only know how to be a beggar! If you heal me I won't know what to do!" and Jeshua did it anyway. Typically there is a higher understanding going on for the greater community when this happens - it's not just overiding someone for our own ego's sake (i.e. "Look what I can do!").
So fast or even instant healing has always been possible. Now with the shift in consciousness, more people will be allowing for that possibility, including people who have had serious, deadly diseases. I know one person who has consistently eluded death from brain cancer - she listens to the doctor's and uses what she feels is appropriate, but has a her own vision of her life beyond what they tell her. And there will still be some people, for whatever reason, who are holding onto their old version of themselves.