Some anime have little or no blood in situations where you’d think somebody would be bleeding, but at the other extreme are the ones where people bleed far too much.
Bleach is a great example since it’s not uncommon for someone to lose a lot of blood at the beginning of a long fight. In theory the anatomy of a spirit body could be different enough to justify it, but no, they actually have a similar structure to a flesh and blood body, with bones, muscles, and organs. In a long fight, someone might lose a liter or more. Yet nobody ever dies from blood loss. Here’s a somehow non-fatal blood geyser.
Zoro from One Piece regularly loses even more blood than a Bleach character, and is even specifically said to have lost 3 liters of blood in one fight, and then 5 liters in another fight only a couple of days later, but he never seems to suffer from not having enough blood either. For comparison, the amount of blood in the average adult human body is about 5 liters. (Sanji, on the other hand, almost died from a nosebleed, so at least the possibility that losing blood could be fatal is acknowledged in One Piece.)
Maybe better not to take that one too seriously…
In Evangelion, we see similar things happen with giant Angels and organic mecha; it’s really messy for Toyko-3, but again, nothing ever dies specifically from blood loss.
For the most part, what we have here is two deviations from reality, in opposite directions; the wounds shouldn’t be bleeding that much in the first place, but the effect of blood loss is downplayed so much that the wounds are still often less serious than they probably would be in real life.