Many people question God's judgements when it comes to the Exodus. Mainly atheists who arrogantly assume they know better than God, but even a Christian might wonder if Pharaoh got the duff end of this deal? Time and time again, we see that God Himself both promised to harden Pharaoh's heart, and that He fulfilled this promise. Furthermore, we see that God did this for His own glory, so that the rest of the world would know who He was.
As Christians, we recognise that God's thoughts are higher than our thoughts. As a child might question the legitimacy of feeding them yucky food, so also do we question some of God's more inexplicable actions. The fact is, none of us are even remotely qualified to stand over God in judgement. Not even a single one of us would win an argument against Him, and as shown by Job's example, we would actually walk away from such an argument feeling pretty stupid.
Nevertheless, as much of a right as God has to just say "I'm God, you're not, shut up and let me do my job", He doesn't necessarily forbid us from asking legitimate questions. And in this case, at least, we do have an answer. Put simply, Pharaoh didn't get any less than He deserved.
The first thing to note is that, ultimately, the moment you choose to sin, you accept the full consequences for that sin. Long before Moses met Yahweh, Pharaoh had enslaved and oppressed the Israelites, such that they had cried out to God. In fact, the whole reason God was talking to Moses was because "I have surely seen the oppression of My people who are in Egypt, and have heard their cry because of their taskmasters, for I know their sorrows. So I have come down to deliver them out of the hand of the Egyptians, and to bring them up from that land to a good and large land, to a land flowing with milk and honey, to the place of the Canaanites and the Hittites and the Amorites and the Perizzites and the Hivites and the Jebusites." (Exodus 3:7-8, NKJV). So, even lacking God's hardening, Pharaoh already deserved punishment.
Furthermore, we see in Romans 1 that those who reject God, God ultimately rejects also. When people do not honour God as God, God gives them over to their unclean desires, and their foolish hearts are darkened. With God, things really are black and white. While He does offer grace, ultimately, you either choose Him or evil, and if you choose evil over Him, there is a high chance He will give you over to evil. In Exodus 5:2, we see that this is exactly what happens. In Exodus 5:2, long before any hardening of hearts had happened, Pharaoh arrogantly announces "Who is the Lord, that I should obey His voice to let Israel go? I do not know the Lord, nor will I let Israel go."
This is what is known as "judicial hardening". We know that salvation is by grace. God does not owe a sinner salvation, but by His grace, He may offer it if He so desires. No one earns salvation. But hardening is earned. Those who sin and reject grace can be justifiably left to their own sin. As I have said before, convincing a sinner to repent is difficult, but to harden a heart, all God needs to do is step out of the way and let a man's nature take its course.
Speaking in His omniscience, God shows that this is exactly what He did. In Exodus 3:19-20, God tells Moses "I know that the king of Egypt will not allow you to go, unless he is forced by a strong hand." From beginning to end, Pharaoh had no intention of releasing Israel. Rather than questioning why God would harden Pharaoh's heart, we should actually be able to see that the only possible way Pharaoh would have obeyed was if God Himself had softened it. Thus, this whole situation falls under the category of God using sin sinlessly. Rather than extending grace to a rebellious king, He instead revealed His glory for thousands of years to come by letting that king play the game he wanted to play, and losing to the better player.