Short answer: regicide ain’t easy.
Long answer:
Regicide ain’t easy because assassinating a King within the confines of his own castle is just always going to be a very difficult thing to do. Kings have castle guards, they have taste testers, and they have the Kingsguard, a group of highly-skilled, duty bound warriors to protect them everywhere they go. This is why Aerys died the way that he did; he was left in a largely unguarded castle with only one Kingsguard knight, Jaime Lannister, to protect him, and it was that Kingsguard knight that turned against him. Jaime had the motive to kill Aerys, and so he did.
Looking back at the previous kings, only two have died due to assassination: Aegon II and Joffrey Baratheon, both by poisoned wine. The other kings who did die early died in battle or as a consequence of war, died of an illness, or in a special circumstance, such as Baelor’s starving himself to death, Aegon V’s death at Summerhall, or Robert’s death by boar (which is partly an assassination, partly an act of nature).
As for why no one killed Aerys before, it was because no one could. The Defiance of Duskendale put Aerys very close to death. He had arrived at Duskendale (thus, he left the safety of his castle) with a small group of men and only one Kingsguard knight, which made kidnapping and imprisoning him an easy feat. It is after Duskendale that Aerys began to slip into madness and became very, very insular. Here’s how it’s outlined in A World of Ice and Fire:
“After his release, King Aerys would no longer allow himself to be touched, even by his own servants. Uncut and unwashed, his hair grew ever longer and more tangled, whilst his fingernails lengthened and thickened into grotesque yellow talons. He forbade any blade in his presence save for the swords carried by the knights of his Kingsguard, sworn to protect him. His judgments became ever harsher and crueler.
Once safely returned to King’s Landing, His Grace refused to leave the Red Keep for any cause and remained a virtual prisoner in his own castle for the next four years, during which time he grew ever more wary of those around him, Tywin Lannister in particular. His suspicions extended even to his own son and heir. Prince Rhaegar, he was convinced, had conspired with Tywin Lannister to have him slain at Duskendale.”
He also had taste testers for his food, yet still ate very little.
So realistically, the only way Aerys could be killed was if he left the Red Keep with too few people to defend him which 1) he never left the Red Keep and 2) the one time he did, it was to attend the Tourney at Harrenhal where he felt that Rhaegar was planning to betray him, and it was with the entire Kingsguard and a large escort otherwise at his disposal.
Moreover, hiring an assassin or using poison is not an acceptable way of moving onto the heir. There is a reason why Rickard was forming a power bloc, and a reason why Rhaegar didn’t depose his father at the first opportunity. An effective transition of power requires the aggressor to have plenty of political and military power at his back. It requires them to have some form of popular support. It requires a measure of transparency. Only that way could their usurpation be considered honorable, because it gives the one being usurped a chance to fight back and know his aggressors. Otherwise, you get what happened with Aegon II and Joffrey’s deaths: a rush to find the perpetrator, arresting innocent people and branding other innocent people as murderers. It is not peaceful, it is not legal, it is not honorable, and should the Tyrells ever be exposed for it, they’d have to deal with massive political backlash that could very well be the end of them.