I dunno. Maybe I'm never unprepared enough to fight a war alongside an ally, but I do find myself overwhelmed fighting two neighbours (an enemy plus their ally) at the same time without an ally of my own.
There are some interesting dynamics with 'Alliance' wars, which I saw explicitly illustrated in my last game.
Tecumseh and Himiko were allied for virtually all of Antiquity and Exploration Age. Went to war with them three times during those Ages. In two wars, had Battuta as an Ally, but he was on the far side of the continent from me: not ONCE did our units ever cooperate in anything. I don't think I even saw more than 3 of his military units besides Scouts.
On the other hand, Tec and Him didn't cooperate either. They never took a city from Bat, and he had several in extremely vulnerable positions. They never even invaded me, except with scouts and single units, but after the first two wars had given up 3 cities to me in peace deals - without me ever threatening them at all.
Pachacuti, my immediate neighbor to the south, joined their alliance in the first war. We stared at each other across a Navigable River for 10+ turns and made peace. Never so much as shot an arrow at each other. Since then we have been neutral or friendly with each other.
Lessons: (reinforced, because I've seen them before)
1. Allies are mostly handy for dividing the enemy's attention. I have never seen even a 3+ Civ coalition make major attacks on more than one opponent at a time, so either they pile onto you, or ignore you while they try to pile onto your Ally.
2. Alliances of AIs are really bad at cooperating. When I have seen armies from two Civs try to attack, they spend a good deal of time getting in each other's way. Mind you, the same thing can happen with your AI Ally, since the detailed planning of the Joint Allied Command in WWII is utterly un-modeled in Civ and always has been. There is no provision at all for putting your units under another Civ's command or vice-versa, and all the political problems that can arise from that (read up on Montgomery' relationship with Eisenhower in WWII, or Deighton's scathing critique of Churchill's relationships with the Australian and New Zealand governments). The Great Elector's maxim is apparently part of the Civ design canon:
"Alliances, to be sure, are good, but forces of one's own are still better" (1667)
3. Just by being part of a war, regardless of what, if anything, you actually do and totally regardless of any threat you ever posed, can still get you settlements in a Peace Deal. By the beginning of the Modern Age in that game, after 3 'major' (alliance) Wars, I had 3 cities that had been gifted to me in Peace Deals, one settlement that 'flipped' to me in the Antiquity Crisis period, and 2 cities that I actually took with military forces (in the third war). Just hanging around the edges of a war can be as lucrative as actually fighting one.
- And, by the way, 2 of those gifted settlements were in Distant Lands, so after converting them to my religion they gave me almost half the points I needed for the Exploration Military Legacy path - basically, without firing a shot!