In Jesus' day, of course, all people needed was Moses and the scriptures from before the time of Christ--not heretics like Jesus or His followers, and certainly not His ordained but fallible apostles who could be and were rejected or criticized on numerous counts.
Elijah, Isaiah, Samuel, and Moses, for example, all were easy to criticize and reject.
Rejecting the messengers the Lord sent is a deceptively easy path to righteousness, or rather, an easy path to self-righteousness. False prophets need to be rejected, of course, but the common instinct to reject the very notion of modern prophets and apostles does not necessarily put you on the winning side of this debate, and may put you among those spoken of by Jesus:
Wherefore, behold, I send unto you prophets, and wise men, and scribes: and some of them ye shall kill and crucify; and some of them shall ye scourge in your synagogues, and persecute them from city to city...Rejecting modern prophets and apostles avoids the challenges of unsanitized, recent history. Recent history comes with the burden of conflicting accounts and witnesses, such as the witnesses who claimed to have seen the Resurrection faked or who claimed that Jesus was a sinner, or who could not accept that the son of a local carpenter could also be the Son of God. It comes with accounts of those who knew and disliked Peter or Paul or Moses. Claiming to need nothing but Jesus also avoids the challenges of dealing with mortal weaknesses in leaders and prophets. No need to explain or excuse the apparent blunders of Peter, Paul, or Moses. It's much smoother sailing with nothing but Jesus.
-- Jesus Christ, in Matthew 23:34
Ironically, the "nothing but Jesus" mantra does not come from Him, just as the doctrine of "nothing but the Bible" is a most unbiblical addition to the words of scripture. Christ told us that he would send prophets. His Church was organized with apostles and prophets in it for a sacred purpose:
11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers;The day of unity has not yet come, thus there remains a need for prophets and apostles in His Church. The world despises modern prophets, as the early prophets and apostles knew so well. But Paul warned against these, teaching us to "despise not prophesyings" (1 Thessalonians 5:20). The principle of ongoing revelation through living prophets is an ancient and true pattern in God's dealings with man. Indeed, Amos wrote that "Surely the Lord GOD will do nothing, but he revealeth his secret unto his servants the prophets" (Amos 3:7).
12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ:
13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ:
14 That we henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive;
It is comforting to think that we don't need to look to any other humans for help or guidance, that it's just us and Jesus, a viewpoint which I fear may be a step close to human self-sufficiency than its proponents will admit.
Jesus, on the other hand, made a great point of organizing disciples and establishing the principles of authority and ongoing revelation to guide His Church. "As my Father hath sent me, even so I send you" (John 20:21). Prophets and prophecy were important before He came. They were important while He was here. And the scriptures tell us they will continue to be important right up to the end. For example, in the book of Revelation, in chapter 11, there is a prophecy of what will be happening in the last days in Jerusalem, right before the Second Coming of the Lord. Two witnesses of God will be killed in Jerusalem. These two witnesses are described as prophets, and they will be prophesying. Most people will reject them. Will you? Will you be among those who say that there can't possibly be any more prophets from God, and that you don't need further witnesses/prophets and their message because you've already got the Bible and Jesus and need not a word more?
Prophets and prophecy will still be going on right up to the end. Angels will still be involved in the work of bringing the Gospel message to the earth (Rev. 14:6) - something even more sure to be mocked and rejected than the concept of prophets. Pity the Church that dares to declare that angels still speak and that prophets still speak. Worst of both worlds. In fact, something not of this world at all.
Yes, as a Latter-day Saints there are many angles from which modern prophets can be attacked, and there are reasonable points of view among those who have examined the Church and rejected its claims. I would say that the arguments commonly used to reject Joseph or Gordon B. Hinckley or others can be effective - so effective that they could also reject fallible mortal prophets of the past like Abraham the polygamist, Joshua the easily tricked (see Joshua 9), Jonah the irritator of endangered whales, or Paul the annoyingly long speaker who killed a man from speaking too long. Don't forget to add Jesus to that list, the Man who offended many and was found guilty of serious crimes by the most respected political and religious leaders of His day. He did not live up to the preconceived notions others had regarding a prophet or the Messiah, and the combination of paradigm-breaking words and deeds coupled with conflicting reports, allegations, and theological misunderstanding made following Him a difficult matter that required great faith. It's still that way today.
Feel free to reject the very concept of modern prophets and believe it's just you and God, or even just you, but don't be deceived into thinking that you have a theologically fireproof position or that you have nothing to defend. Rejecting those whom God sends does not somehow give you a pass or make you spiritually superior.
If you are a serious Christian but, for various reasons, reject Joseph Smith and what I believe to be the restored Church of Jesus Christ, I think it would then be appropriate to consider where to look to find authority and modern revelation on the earth, rather than assuming that we must not need prophets and apostles anymore just because we don't seem to have them. Perhaps you will look to Roman or Orthodox Catholicism, or some other source. But I suggest you look, think, and search with an open mind, and not fall into what I consider to be the deceptive trap of thinking that you need nothing more than what you have. Keep seeking!