I agree with you here. God does demand that His creatures love, worship, praise and give thanks to Him. However, I strongly disagree that the "natural man" can do these things. If man could, then God would have not had to devise a plan for Salvation. Additionally, this flies in the face of what Holy Scripture says about the natural man.
Rom 3:9b ..for we before laid to the charge both of Jews and Greeks, that they are all under sin;
Rom 3:10 as it is written, There is none righteous, no, not one;
Rom 3:11 There is none that has understanding, There is none that are seeking after God;
Rom 3:12 They have all turned aside, they are together become unprofitable; There is none that does good, no, not so much as one:
Rom 3:13 Their throat is an open sepulcher; With their tongues they have used deceit: The poison of asps is under their lips:
Rom 3:14 Whose mouth is full of cursing and bitterness:
Rom 3:15 Their feet are swift to shed blood;
Rom 3:16 Destruction and misery are in their ways;
Rom 3:17 And the way of peace have they not known:
Rom 3:18 There is no fear of God before their eyes.
1Co 2:13, 14 Which things also we speak, not in the words which man's wisdom teaches, but which the Holy Spirit teaches; comparing spiritual things with spiritual. (14) But the natural man receives not the things of the Spirit of God: for they are foolishness unto him: neither can he know them, because they are spiritually discerned.
Jer 17:9 The heart is deceitful above all things, and it is exceedingly corrupt: who can know it?
These are just a few of the Holy Words about the natural state of fallen man.