I will have to disagree on your Khuda concept of being the greatest. My reason simply are if your thirsty then you must go to the well, the well will not come to you to quench your thirst. You make the effort go to the well or tap get a glass of water, then drink it by first saying Bismillah, then drink in short 3-4 gulps. Once finished you say Alhamdulillah, the water did not quench your thirst, your effort then starting with Bismillah and ending with Alhamdulillah, Allah SWT quenched your thirst. So yes in this case you do have to do something for something to happen for you, you have to invoke, remember, beg and thank Allah SWT.
If we were getting blessings from Allah SWT by just Khud-a as you put it then why would we have to ask and then thank Allah SWT, since everything is blessed from Allah SWT. To get food on the table of course you have to work for it if you are capable of working, if in that case you just begged people on the streets, because of laziness and ease, thats the type of begging Allah SWT does not like. He never said dont beg Him, we must beg for Allah SWT's mercy all the time even though hes the most merciful.
People have many needs some right and some wrong, often people blinded by their ignorance or lack of knowledge will ask for wrong things, such as a long life or huge amounts of wealth, just to live longer and indulge in worldly pleasures, these types of people's hearts get sealed.
Beloved Prophet Mohammed PBUH was standing at Mairaj once HE PBUH saw many things going up and many things coming down. Prophet PBUH asked Jibrael AS, what are the things going up and whats coming down. Jibrael AS explained the things going up are people's deeds, the things coming down are decisions from Allah SWT.
Allah SWT knows best.