It had been ages since I last tried it out, having given the date picker a go when it was new and shiny. What the feature says on the can is "You can now select dates from a date picker. The cell must be date formatted."
Well strictly speaking this both is (and isn't) true. As I recall originally when first introduced yes the date picker worked but only on plain formula free input values and not on DBR/W cells. (My memory from 2 or 3 years ago might be a bit hazy but that's what I recall. I'm happy to be corrected). As we might say in the colonies that makes said feature about as useful as tits on a bull. Because surely the whole point is to guide valid data entry into your TM1 application? Like a picklist? ... Maybe something was missed when briefing the developer.
Also maybe in the meantime this has been addressed and it now works for DBR/W cells? To test this theory I just tried it out on the very new and shiny PAL 2.0.5. Yes the date picker does work in the latest version on DBRs. Except when it doesn't! The date picker itself "works" and continues to work (as in the date picker UI displays and the cell value can be changed) but the linked cube cell value is only updated on the first value change. In other words the update of the date value nukes the DBR and the link to the model.
Curiously this behavior seems to be an artifact of the test case I created that had multiple cells pointing to the same cube cell (since I was testing which date formats are recognized by TM1 Web for the date picker, e.g. yyyy-mm-dd, dd mmm yyyy, dd/mm/yyyy, mm/dd/yyyy, etc.) As long as only one cell is ever used for updating the cube continues to update. But as soon as multiple cells pointing to the same cube cell on the same websheet get used then it all breaks.
So still a bug. But not quite so potentially disastrous.