Why does/would a "Bodhisattva" burdens himself and instigate others as well? Why does/would a "Bodhisattva" burdens himself with the choice of becoming a Buddha (avoiding extinguishing dukkha) and instigate others as well to do so?

Given that this world is full of "Bodhisattvas", there is not one being who is not just here to help others out, why does a Bodhisattva instigate others to stay on this normal course of birth and death?

Does he need food to nourish his undertaking and fearing to find nobody and nothing as reason for further becoming?

Or what is the reason to instigate others to do such a work?

Just to become one day wise and listen to what the Buddha say and trap others who have the same blindness for it? (Given that the Teachings of the Buddha of our time is still available)

Or do they assume that there are no teachings which lead them out for now?
A Bodhisattva 'instigates' others because he wants what is best for others (full enlightenment together with its causes). From this viewpoint, 'abiding nirvana' is thus not what is best for others,  because it is not the one final result of the one final vehicle (i.e. the Mahayana path).

There are two obscurations:


Afflictive obscurations - all the afflictions - which prevent one from achieving abiding nirvana, and 
Knowledge obscurations - the imprints left by previous moments of ignorance - which prevent one from achieving perfect enlightenment, omniscience.


If he completely abandoned afflictive obscurations (which an arya bodhisattva does anyway from the 8th  bhumi), the practitioner would be free from the conception of inherent existence, but he would not be free from the appearance of inherent existence because such a mistaken appearance is  caused by knowledge obscurations. A bodhisattva does not aim at merely abiding in 'abiding nirvana', but wants to be completely free from all mistakes and thus be able to enact the welfare of others.

The bodhisattva does not set out to merely get rid of afflictive obscurations and achieve abiding nirvana. He set out, from the entry into the Mahayana path, to get rid of knowledge obscurations and achieve what Mahayana call 'full buddhahood', 'perfect enlightenment', 'omniscience', 'the four kayas', 'non-abiding nirvana'.

The wisdom directly realizing emptiness is said to be 'the mother of all three types of enlightenment - that of the shravaka, the pratyekabuddha, and the bodhisattva' because it is a cause of enlightenment. However, it is a Mahayana belief that full enlightenment (that of the arhat-bodhisattva, an arya buddha) can not be achieved by cultivating the wisdom-side alone. One needs the method-side, namely bodhicitta, the six perfections, and so forth.

Knowledge obscurations can only be removed by way of developing the two wings that are method and wisdom. When the wisdom directly realizing emptiness is conjoined with bodhicitta, that wisdom becomes what is called 'ultimate bodhicitta' and that puts an end to what prevents one from achieving omniscience, the omniscient mind of a buddha, buddhahood, perfect enlightenment. That is why a bodhisattva cultivates bohdicitta, which is 'the wish to achieve enlightenment for the benefits of all sentient beings'.

The classical analogy goes: the wisdom realizing emptiness is like an axe while bodhicitta is like the strong arm. You need both the axe and a strong arm to cut the tree (that is here knowledge obscurations).

We say that from the path of seeing, an [arya] bodhisattva comes back in samsara but is not wandering in samsara. So his aggregates are not contaminated anymore, and there is no 'true suffering' involved. It is not the case that he will suffer for eternity. This is because he does not come back under the power of karma and afflictions, but under the power of compassion and aspirational prayers.