Given how Obito had acquired Bijuu in the past, why would he bother going to war? I don't get this.

Did Obito think that it would be easier to go to war with the whole shinobi world rather than capture the 8-tails and 9-tails Jinchuuriki on the low like how he did with the other ones?  He basically ended up fighting not only both of them but also the entire shinobi world. 

Would Obito's plans succeeded if he did not declare war and kept everything under the radar till the end?  I believe he'd have been successful and that he wouldn't have needed to summon Madara at all.
Obito declared war because he knew that the alliance would keep Bee &amp; Naruto at a disclosed location since they had caught on to what the Akatsuki were doing. The war would allow him to draw out Naruto &amp; Bee to complete the plan of bringing back Ten Tails in it's prime state.

He had Kisame gather intel, but then of course Kabuto showed up. Obito's plan was essentially to gather intel on the locations of the last two jinchuuriki, use the zetsu to distract the allied shinobi forces in a war, and lure Naruto/Bee out. It didn't work out like that, but he had a legit plan.