Answer

1. In any case, it is not certain that a poor person will knock on his door, so even if there were an obligation to give to every poor person, this is still only a doubtful gain. Therefore, even if he is not obligated to give to every poor person, there are still situations in which he is obligated, and in those situations he is exempt because he is busy with the lost object. That alone is enough to make him a paid bailee.
2. A paid bailee is not necessarily required to guard more carefully. Simply speaking, he too guards in the normal way people guard. It only adds liabilities if something happens (theft or loss). The discussion is not about what he deserves, but about which legal category he falls into. If this thing is indeed considered payment, then he is a paid bailee. Even if morally it seems unfair to you, that is the legal situation. The Sages can always enact a regulation exempting those who guard lost objects because of the moral consideration. The discussion here is legal, not moral. Now I find myself wondering whether a paid bailee can make a stipulation like any other bailee can (Mishnah, Bava Metzia 94a). Seemingly, he could accept upon himself to take care of a lost object on condition that with respect to it he will be only an unpaid bailee. This requires discussion, because there is no second party here. He cannot stipulate with the Torah, since it obligates him. This is not a voluntary contract like an ordinary bailee, where everything is in his hands. On the other hand, he can choose not to involve himself with the lost object. This is a halakhic obligation, not a legal one. Therefore perhaps he actually can make such a stipulation. Like the stipulation of a person who saves his fellow on condition that he be paid more than an idle laborer.