There are several reasons.
Many factors contribute to why most wizards don’t use Unforgivable Curses in battle, and each individual wizard who chooses not to use them may base their choice on one or a combination of reasons.
Unforgivable Curses are illegal.
Using the Unforgivable Curses is illegal - using any one of them is enough to get a life sentence in Azkaban. Even wizards who are capable and willing to use them may not if they consider the possibility of being sent to Azkaban for life over their use.
“Now … those three curses – Avada Kedavra, Imperius and Cruciatus – are known as the Unforgivable Curses. The use of any one of them on a fellow human being is enough to earn a life sentence in Azkaban.”
- Harry Potter and the Goblet of Fire, Chapter 14 (The Unforgivable Curses)
That’s likely a very strong deterrent to using them, even in serious situations, since no one wants to go to Azkaban. It also would work on some wizards who’d have no other problems with using Unforgivable Curses, because the consequences are extreme.
They’re difficult to cast.
Additionally, only wizards with a certain level of skill and power can cast Unforgivable Curses. As Snape tells Harry, casting Unforgivable Curses requires both nerve and ability.
“Cruc—’ yelled Harry for the second time, aiming for the figure ahead illuminated in the dancing firelight, but Snape blocked the spell again; Harry could see him sneering.
‘No Unforgivable Curses from you, Potter!’ he shouted over the rushing of the flames, Hagrid’s yells and the wild yelping of the trapped Fang. ‘You haven’t got the nerve or the ability –”
- Harry Potter and the Half-Blood Prince, Chapter 28 (Flight of the Prince)
“Nerve” likely refers to the desire to use the Curse, something that’s particularly important with the Cruciatus Curse. Crucio can cause varying degrees of pain, and the more you want to cause pain, the more effective it’ll be. A Cruciatus Curse that doesn’t have that desire behind it will be ineffective, so wouldn’t help much in a battle.
“Hatred rose in Harry such as he had never known before; he flung himself out from behind the fountain and bellowed, ‘Crucio!’
Bellatrix screamed: the spell had knocked her off her feet, but she did not writhe and shriek with pain as Neville had – she was already back on her feet, breathless, no longer laughing. Harry dodged behind the golden fountain again. Her counter-spell hit the head of the handsome wizard, which was blown off and landed twenty feet away, gouging long scratches into the wooden floor.
‘Never used an Unforgivable Curse before, have you, boy?’ she yelled. She had abandoned her baby voice now. ‘You need to mean them, Potter! You need to really want to cause pain – to enjoy it – righteous anger won’t hurt me for long – I’ll show you how it is done, shall I? I’ll give you a lesson -”
- Harry Potter and the Order of the Phoenix, Chapter 36 (The Only One He Ever Feared)
Avada Kedavra has only two possible effects - it either works or it doesn’t, it can’t kill someone any more dead if cast more skillfully than necessary, but it takes a certain level of skill and power to cast it effectively. If it fails, then it fails entirely.
“Avada Kedavra’s a curse that needs a powerful bit of magic behind it – you could all get your wands out now and point them at me and say the words, and I doubt I’d get so much as a nose-bleed. But that doesn’t matter. I’m not here to teach you how to do it.”
- Harry Potter and the Goblet of Fire, Chapter 14 (The Unforgivable Curses)
For a wizard that’s not skilled enough to use the Unforgivable Curses, it’d be more effective to cast a spell that they’d be successful at using that attempting to use an Unforgivable Curse unsuccessfully.
They’re also considered immoral by some.
Furthermore, some wizards wouldn’t want to use Unforgivable Curses at all, even if using Unforgivable Curses wasn’t illegal and they were skilled enough to use them. Dumbledore avoided using Dark magic entirely.
“I know you haven’t,’ said Professor McGonagall, sounding half-exasperated, half-admiring. ‘But you’re different. Everyone knows you’re the only one You-Know – oh, all right, Voldemort – was frightened of.’
‘You flatter me,’ said Dumbledore calmly. ‘Voldemort had powers I will never have.’
‘Only because you’re too – well – noble to use them.”
- Harry Potter and the Philosopher's Stone, Chapter 1 (The Boy who Lived)
It’s very rare to see a member of the Order use an Unforgivable Curse, which is likely at least in part to a desire not to use Dark magic. Moody, a member of the Order of the Phoenix, also had a similar set of beliefs as an Auror - he avoided killing, and likely Unforgivable Curses as well.
“I’ll say this for Moody, though, he never killed if he could help it. Always brought people in alive where possible. He was tough, but he never descended to the level of the Death Eaters.”
- Harry Potter and the Goblet of Fire, Chapter 27 (Padfoot Returns)
Sirius Black, another member of the Order, thought Barty Crouch Sr. went too far in his attempts to capture Death Eaters using violence against them, which included allowing Aurors to kill and authorizing them to use the Unforgivable Curses.
“Crouch’s principles might’ve been good in the beginning – I wouldn’t know. He rose quickly through the Ministry, and he started ordering very harsh measures against Voldemort’s supporters. The Aurors were given new powers – powers to kill rather than capture, for instance. And I wasn’t the only one who was handed straight to the Dementors without trial. Crouch fought violence with violence, and authorised the use of the Unforgivable Curses against suspects.”
- Harry Potter and the Goblet of Fire, Chapter 27 (Padfoot Returns)
Harry, Ron, and Hermione all seem very reluctant to kill Antonin Dolohov and Thorfinn Rowle, both notorious Death Eaters. Ron brings up the idea, but is clearly relieved when Harry rejects the idea. Hermione shuddered at the thought of it.
“What are we going to do with them?’ Ron whispered to Harry through the dark; then, even more quietly, ‘Kill them? They’d kill us. They had a good go just now.’
Hermione shuddered and took a step backwards. Harry shook his head.
‘We just need to wipe their memories,’ said Harry. ‘It’s better like that, it’ll throw them off the scent. If we killed them, it’d be obvious we were here.’
‘You’re the boss,’ said Ron, sounding profoundly relieved. ‘But I’ve never done a Memory Charm.”
- Harry Potter and the Deathly Hallows, Chapter 9 (A Place to Hide)
So, that’s yet another reason why the average wizard wouldn’t use Unforgivable Curses - some consider it wrong. Also, those who consider it wrong to use Unforgivable Curses are likely to be less effective at casting them, even if they tried, as they mightn’t be able to put enough power behind the Curses to cast them well.