Is God willing to save all?  Yes!

The Lord is not slack concerning his promise, as some men count slackness; but is longsuffering to us-ward, not willing that any should perish, but that all should come to repentance.  (2 Pet 3:9)

To the same degree that salvation and eternal life are available to all men, physical healing is also available.  Both salvation and healing are a part of the same redemption. 

Jesus healed ALL who came to him.  He never turned away a sick person, nor did He ever explain their sickness as a necessary part of their spiritual growth.   He never made anyone sick, nor did He ever tell someone to wait for their healing until some condition was met.

How God anointed Jesus of Nazareth with the Holy Ghost and with power: who went about doing good, and healing ALL that were oppressed of the devil; for God was with him. (Acts 10:38)

It was James understanding that there should be NO sick believers.

Is ANY sick among you?  Let him call for the elders of the church; and let them pray over him, anointing him with oil in the name of the Lord:   And the prayer of faith shall save the sick, and the Lord shall raise him up; and if he has committed sins, they shall be forgiven him.  (James 5:14-15)

Will God honor His Word?

And all things, whatsoever ye shall ask in prayer, believing, ye shall receive. (Mt. 21:22)

It doesn’t say ‘all things except some sicknesses.’  Anything that doesn’t reflect the nature of God Himself is something that you can be delivered from.  There is no sickness in God.

Every good gift and every perfect gift is from above, and comes down from the Father of lights, with whom there is no variation or shadow of turning. (James 1:17)