The problem here is the word "can".
"Can" spiritual advancement make someone able to heal all illnesses? Yes, of course. Spiritual advancement can even make someone physically immortal, if high enough.
"Can" the person reading what you would've said do this? No. Not even "most likely", just no. The number of people that can do real spiritual healing here is quite low, as this takes a lot of power and experience. And even then, from "can do spiritual healing" to "can heal any illness", is yet another long road still.
This kind of statement doesn't do much good, and does a lot of bad. Of course spiritual advancement will bring one blessings that one could only think of as miracle.
But when we speak, we need to understand that there is no such thing as "naked fact". The words we speak have consequences.
Someone here could be delusional about their level of spiritual advancement. Then, they read such a statement, and they have this or that chronic illness that requires medicine, or this or that acute problem that requires treatment, and they instead choose to trust spiritual powers that they don't actually have. Bad result.
Spiritual healing is important to not forget. Yes, if you have a solid level of experience with meditation practice, you should start doing workings to improve your health. Yes, if you have the common cold and a couple GOOD years of meditation behind you, do try to send healing energy and heal the cold faster.
But let's not go into New Age "name it and claim it" nonsense.
If you have diabetes, you do not need spiritual healing, you need insulin. You need insulin NOW, which will ALLOW you to then spend more time advancing to eventually, hopefully, heal this diabetes (yes, never rule things like that out as a possibility, as long as you are still taking your medicine)
If you have a bacterial infection that requires antibiotics, you are (and this is being generous) perhaps 10 years away from having the power to combat bacteria "spiritually". And yet, if you don't go to a doctor and take antibiotics, you have a week-long clock ticking to your DEATH.
These things are serious. As HPS Lydia Coventina stated above, HPS Pythia has always been adamant about the fact that modern medicine (with its faults, yes) is a great advancement for humanity that must be taken advantage of, as it saves lives that would've otherwise been lost.