Two things:
1. *They will die when stripped of their Bijuu and those with exceptional life force will be left in a weakened state.
2. They shouldn't have to exit their village. If, say, Eric was still in Konoha and he publicly RPed in Konoha within the required time limit, then there is no need for him to exit the village. Why would he need to in the first place? To make it easier on hunters? If so, that's stupid. It was hard for the Akatsuki in the series so it shouldn't be any easier for players especially since most Jincuriki leave their from time to time. I did it some of the time, Kirk did, Eric did/is, etc.
Requiring the jincks to leave their village, at a single time of the month or so, is not really asking that much. No one ever said that they had to leave alone; you could still have an entire escort of shinobi that are just as capable of defenders in the field as they were at home. Going into their local countryside like Konoha Forest in your example is good enough.
The point of that argument is, in a sense, to make it just a little easier on the hunters; the jinck could still carry around a huge load and rear guard, but at least the battle would not be in the village were there to be a huge strew fest. As anyone involved in hosting and challenges know, biju battles can get rather heated if you put the right people in the mix.
At least, if they have left their village, people can still leave the village in order to help them out should the time occur (and they're just talking a stroll in the surrounding countryside), so saying that the jincks would be much more poorly defended is a load even a whore shouldn't have to swallow, unless the village has hax barriers and such.
Another part of this was to prevent hoarding from extending to hosts. Yeah, I get it, it's totally a fair option to tell the jinck that they can't leave, the series shows that. But, at the same time, the series also shows how unpractical that is, especially if the jinck is on the stronger side.
There are no rampant shinobi wars going on right now, and missions are hardly a cut-throat occupation, making the hunter have to go through not just the people, but the walls, the buildings, and literally make them destroy the village just to have a chance at the tailed beast is quite ludicrous.
Not just for the hunter(s), but even for the villagers themselves. The Kage wants to hoard the beast in the pot smoker down in the basement; Bocc returns to SL (most lucid example that comes to mind atm) with an army of stone shinobi and derp rushes the village. Now the entire village is caught up in this, and in one way or another, it forces everyone in the village to participate one way or another in the biju game.
Large RP's nowadays, fail, and it is not always just because of how long it takes people to post (though that's part of it) and RL getting in the way (a big part of it). Some would say "Well, they can just post doing something else somewhere else".
Well, no, not really, we all know the style in which Bocc (or anyone attacking a villager) would go, if given the chance, he would bring the entire village to bear just to repel; no half-loyal citizen of any village is going to just go about their daily lives, buying bread and fapping to the Icha Icha series while everything around them is getting shredded in some huge battle.
And if they do... Then their characterization better not even bat an eye if a meteor-sized piece of wood crashes down on their favorite food shop.
Summary:
Making the jincks leave their village/hideout every now and again, for the time listed previously, makes this whole thing fairer for the hunters, and reasonable for the general inhabitants of said village, and it isn't exactly asking for an arm and a leg either.