Of course, we all know, or should know, that all healing is of God, whether a doctor is involved or not. When my pastor's wife had Pancreatic cancer 5 years ago, the oncologist who confirmed another doctor's diagnosis asked her if she believed in God. She told him, yes. He then told her to put her trust in Him, because he [the doctor] could do nothing but relieve her pain. [Many were praying and continued to do so, but about 2½ months after the diagnosis, she was gone. But... she had lived close to God for most of her 90 years. During those last few weeks while enduring severe pain in spite of the best efforts of medicine, she encouraged everyone who visited her advising them all to put their trust always in God.
As to why we should praise God consider the follow verse from Psalms:
"But thou art holy, O thou that inhabitest the praises of Israel." Psalm 22:3
And just who is Israel, but "he that will rule as God"?
"Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel:
Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called." Rom 9:6-7
To me Israel, in addition to being the natural sons of Jacob in the OT, is God's chosen people at any time. If we are His people and we praise Him, will not He be inhabiting our praises?
Why praise God indeed? Why pray? Why trust in God for anything? When God is limited, is it not people who limit Him?
"Yea, they turned back and tempted God, and limited the Holy One of Israel." Psalm 78:41