The led lamp could be a 5v one , or anything up to a 50v one. we sometimes need the power drain from the battery to be 1w, sometimes 2w, 0r 3w, 0r 5w, and so its easier to regulate the battery current. We know the battery voltage (micro ADC), and so the micro can then just set the current for 1w, 2w, 3w or 5w operation, as required.
also, it makes the feedback loop easier to stabilise...this is because the feedback loop doesn't know its a sepic converter, as the output doesn't appear in the feedback loop.....as far as the feedback loop is concerned it could be a sepic or a boost converter , or a flyback, or in fact. it could just be an inductor with an antiparallel diode across it.
Also, the input is low voltage , and you can get lots of capacitance there without needing to use electrolytics.....so you can use longer lasting ceramics. ....The lots of input capacitance will make it more stable.
So the converter is a sepic but doesn't have any of the feedback loop problems/uncertainties of a sepic...if you completely remove the output capacitor it still remains stable.....and this proves that the output is not in the feedback loop.......try stabilising an output voltage regulated sepic with no output capacitance...you won't manage.
Feast our eyes on it because it gives all the advantages of a sepic without the feedback loop problems of a sepic.
So having the feedback loop regulate the input current makes for better stability.......if we want , we can shove in a sense resistor at the output to really finely tune the output current...but its not really necessary.