Puja is structured as hospitality, and once that is seen the sequence stops looking arbitrary.
The classical service offers the deity what a household would offer an honoured visitor, in order: a seat, water for the feet, water to rinse the mouth, a bath, fresh clothing, perfume, flowers, incense, a lamp, food, betel, and finally praise and a formal leave-taking. The lamp is moved in a circle before the image, and worshippers draw the warmth of the flame toward their own faces afterwards. Food that has been offered is returned as prasad, and eating it is the moment at which the worshipper receives something back rather than only giving.
At home this may take two minutes at a shelf of printed images, performed by whoever in the household does it, most often a woman. In a large temple it is performed by hereditary priests at fixed hours, and the image is woken in the morning, bathed, dressed, fed at intervals through the day, entertained, and put to bed at night with the sanctuary closed. Major temples have run that schedule daily without interruption for centuries, which makes the deity a resident with a household rather than a presence that is summoned.
The central act for the worshipper is darshan, seeing and being seen by the deity. It is a visual exchange rather than a verbal one, and it explains a great deal both about temple architecture, which is organised to deliver a sightline, and about the crowds: people will queue for hours for a few seconds in front of an image and regard that as the substance of the visit rather than a disappointing fraction of it.