Well, newcrasher, I hope this helps.
I think that worship services don’t have any single particular purpose; the ones you cited are probably fairly important to most. My own faith is very emphatic on ties between people and ties between the people and the gods; most practices involve one or both of these, which I’d say are of equal importance.
There are some other things to keep in mind, though. Some services are constructed to induce or assist in perpetuating a particular frame of mind; oftentimes those frames of mind are difficult (or perhaps impossible) to create outside the context of shared ritual.
Some religions have practices that include the pooling of knowledge or a division of skills. Call and response services are not uncommon, and have a particular feel to them. Some religions have important things that are structured around enactments of particular rituals – consider Communion in Christianity as an example, or the interactions between High Priestess, High Priest, and the quarters in formal Wicca. A congregation or group of whatever sort provides a continuity of knowledge and the ability to bring new people into the faith smoothly through growing familiarity with the rites and practices.
There is also the support of the community, which is, admittedly, a two-edged sword. There are those people who will use their displays of piety as a play to get status, as the Matthew passage condemns. There are, however, also those people who find comfort in the knowledge of association with like-minded people; humans do have fairly strong tribal tendencies, after all. And these communities often support their members in material ways as well as bolstering spiritual doubt and providing that shared context.
Personally, I’m dubious about setting aside times specifically for the gods as a motivation; it’s a sort of compartmentalisation that I can’t actually pull off. If my gods are not a part of my life with continuity, then a special time for them is fairly hollow. What services do for me are, in part, to make a time where that is a primary focus, not one of the minor incidentals of my life.