Should Jesus have read the whole chapter, or the whole of Isaiah to claim Scripture was being fulfilled?
Read on in Isaiah 61 - the rest of v. 3 applies, & the whole chapter is applied by the Gospel.
Other reason for not reading the whole prophecy could include -
he'd said enough for his hearers to identify the passage & look it up;
he want to stress what he had read about his healing ministry;
he wanted them to think about the very next phrase after they had rejected him;
the beatitudes in the sermon on the mount do include aspects of Isaiah 61, and judgment in hell fire.
When Jesus said, "It is written .... " he obviously expected his hearers to refer to & remember the passage.
It matters very little which scheme one adopts, but what cannot be relinquished is the exactness and reliance upon what has been prophesied about the future based on what has been fulfilled in the past.
Experience indicates that there are those who would see a fulfillment in a portion and then, because the next part doesn't fit some scheme or historical unfolding, suggest that the prophecy must in that portion be taken as differently, or is in some manner to be held less than exact.
Perhaps Augustine struggled over this very issue when trying to come up with answers to what he was seeing both in the Scriptures and in history. Because he was schooled in philosophy and rhetoric, he looked for answers that required him to abandon the facts of Scripture and embrace that of allegorical. It would have been far better for him to not have made such a shift in his thinking.
However, when one removes such thinking, and acknowledges that if for certain (as it was) the Scriptures were fulfilled exactly as stated in the first coming of Christ, then it must be that the promised return will unfold with that same authority.