Well, if you ever needed debug mode, then bughunt mode was definitely called for in case you wanted to avoid cheating. 
Otherwise, the origins of this feature were the OG aliens who loved to hide in some corner of a tiny shed when everyone else had been killed, and the TFTD cruise missions with their 'I will hide in this cubboard all day' critters. It certainly 'made sense' there.
I've also had instances in XCF where bughunt mode has been beneficial, like a ninja strolling in the woods after every other Lotusite has been terminated and I have no scanners on that mission (early game, mostly). Or I missed a sweep due to wacky LoS and some enemy managed to wander off into some labyrinthine building. Or decided to hang out on the map's edge.
Granted, my bughunt mode is a little bit customised, and as the game goes on and especially as psi-vision and scanners come online this is much less necessary.
I've had similar cases with assassins. I perceive it as part of the role-play. Assassins are the main trump card of the lotus. They always cause huge trouble, and often change the game.
If my agents get into an extraordinary situation, I just evacuate them. Sometimes I even use it not quite honestly. For example, the embassy of hybrids. The person above made fun of me, but he doesn't understand the salt of the game at the iron man difficulty level at all. The hybrid embassy is the simplest and safest mission if you fly into a rep with automatic doors. And the reward is just fantastic. For one embassy 20m ~ $, Batarians, ai fragments, alien data. This is the revolution of the whole game. I fly to every embassy up to 10 times for leveling up characters, and for stealing ai fragments. I will never attack the Exalt mansion until it becomes an embassy.
When you get used to playing at the Iron Man difficulty level, the game becomes completely different forever. Problems do not upset, but only become a riddle, which is very pleasant to solve. I conquered my first alien colony only the third time. The first two times I lost my two best teams. It was very dramatic and emotional. Now I am preparing a second attack on the Ethereal base. And I'm not confident in my abilities. But the preparations and the waiting excite the blood in my veins.
And about the search for the last alien, and tftd... This was the last time when I was a child. In oxce, all locations are 4 times smaller than the original locations of the TFTD DOS version. When I passed tftd two years ago, it was an easy walk. The hardest thing is to kidnap Gilman and his corpse on terror. The rest is just fun with underwater blasters and psi disrupters.
