The drilled shaft has to be adequate for whatever lateral loads are applied to it, but it's a pretty common way to do light tower and traffic signal pole foundations. We also go directly from drilled shafts to columns on multicolumn 'bents', where the cap is 12' to 20' above ground.
I haven't designed one, but we have at least one bridge with piers that consist of a series of individual columns on drilled shafts, that each support a bearing for a single girder.
No real reason to have it. I have seen it done both ways, assuming you are in non-seismic country. If you're in seismic, pile caps are recommended in order to tie the various columns together with grade beams or equivalent.
One thing to consider is that the guys installing the piers aren't the same ones doing the superstructure work. It is likely that the superstructure guys will have to have someone layout the column dowels in the pier as it's being poured or risk the pier guys mis-installing it. I have seen jobs where there's been finger pointing because the column dowels didn't get installed into the pier cap correctly.
Caps are standard around the perimeter for grade beam support (at least the way I usually detail it).
For interior caissons, it is now our company standard to provide caps. This prevents the field from having to set anchor bolts over an open hole often 20+ft deep. Not only from a safety perspective, but its also less likely to have an error in layout when you don't have to worry about falling to your demise.
Pier caps are mostly used as a transfer device to allow transition between the circular oriented pier vertical reinforcement and the upper, column (or whatever) reinforcement that is in a different layout/pattern.
If you can accommodate the transition without a cap then there's no issue - but many times the pier, and its reinforcement, is in a significantly different layout than the reinforcement above.
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In most cases, I think that you need a cap of some kind as a transition element to compensate for tolerances in pile and pile rebar installation. It's a bit of a rough thing. The two exceptions that come to mind are:
1) Single element things not too sensitive to tolerances. Poles and such as Hotrod mentioned.
2) In my market, basement walls will be cast right to piles with no grade beam between.
If you are using it to support a steel column which has a finicky anchor bolt pattern or precise top elevation, you might want a cap.
The guys drilling shafts and filling them with concrete are not known for their meticulous handiwork. And they are rightfully allowed pretty generous tolerances.
How meticulous the guys are with setting the anchor bolts usually depends on whether those same guys have to bolt up the pole or column to it later, I suppose. For what we work send out, we haven't had any problems with pole foundations. They typically have a plywood or metal template of the base plate to hold the anchor bolts in place. We've had a few out-of-plumb columns because of misaligned rebar cages, but most are not bad. There again, the GCs tend to watch their subs closely so as to avoid major headaches. Our field engineers keep a close eye them too.
