I like to sand with power on both the lathe and mandrel. I love the power lock system because it has a good resin on resin bond to keep the grit where it belongs, and I don't have to press and build heat for it to work properly. Of course the way I use it, favoring the center of the disk on convex surfaces and the edge on concave means I can re-use it often, and pitch the disk on the shelf without worries that velcro will pick up shavings or chips before I use it again, because it has the locking disconnect. If I do press a bit, there are no plastic hooks to melt.
As to it being inferior in following shapes, I'm puzzled at Steve's difficulty. If no more of the paper is in contact with the work than the width of the bevel that cut it, there's no problem sanding at 3:00 or 9:00 o'clock, and with a 1" radius, sanding at 12:00 will get you into most places a bowl needs sanding, unless it's cut at less than a 1" radius. Further, they make a flexible edge version with the same easy-swap, easy-store characteristics which is great for working in confined spaces, and can be given a "set" to the shape to slide back under the rim of a passing bowl or down to the bottom of a shallow-curve goblet.
The greater rigidity is your friend when you use it to avoid pressing into the work. It's less likely to follow soft spots, serving as if it were a rotating scraper. It heats much less because you don't have to press, and that's the key to greater paper life. I've recently begun using it at 240, rather than transitioning to velcro, but that's as low as I would go. At or about 220 you're removing so little that micro versus macro sanding assumes greater importance. You want to follow the nuances of the grain, for which flexible paper seems better suited. Whatever that green stuff at Packard is, it just hangs in forever. Once again, I don't press, nor do I use passive sanders that rely on friction with the piece.
I'd like to suggest a revision of that oft-repeated "don't skip a grit" phrase. Makes no sense at all, when you consider what you really want to say is that it will take longer to remove the marks from one grit with another if you have too great a difference in the numbers. Of course, the manufacturers help us out by making papers in their own series 80/100/120/150/240/320 for my Power Lock system, where I regularly "skip" 120 if I use 100, and 80/100/120/180/220/320 for the hook and loop I stock, where the 180 or 220 is regularly skipped, depending on where I start. Of course, they may be in different grit systems for all I know, so the 120 hard back may not be the same as the 120 soft.
If you find it's taking too long or building up too much heat to remove the scratches from one grit with another, find and use an intermediate number.
Two other points to ponder on power sanding. You're not limited in the direction you can sand, because you have a rotating piece and a rotating paper. This means you can sand across 12:00 to get rid of tool ridges, instead of at 9:00, where it'd take forever, heat you and the paper, and likely result in an undulating surface at the end. Same applies for the next grit, except if you finished sanding more or less at 9:00, your scratches will closely resemble the tool ridges, only on a smaller scale. I find this change of sanding directions with each grit speeds the process nicely.
Second, you're going to make a lot of dust, and there's no way you want to chew it twice, so on inside sanding, where the dust wants to fling out at the rim, give it a hand by not sanding inward at 9:00 or 12:00. Resanding packs the grit, heats the paper and the piece, so try to avoid it by lifting, wiping, and choosing your directions to favor sanding into the cleaner surface.
