I really don’t think they have any concept of artificial insemination, or even what behaviors result in pregnancy. There is obviously variation between species but I doubt most of them would understand how a pregnancy occurs in the first place, they mostly perform behaviors they have learned from watching their parents or are guided by instinct.
Artificial insemination techniques vary by species, but most techniques are barely more invasive than taking a temperature or performing an internal exam, and most animals resent it less than having their nails trimmed. The exception being surgical AI and there is significant debate about whether this procedure should be done. There’s really not much protesting the actual procedure by the animal when it comes to AI.
As for ‘always wanting to be pregnant’, I really don’t think ‘wanting’ comes into it, because I don’t think they understand it much. There doesn’t seem to be much self-awareness for animals when it comes to reproduction. In ideal wild conditions, they tend to breed quickly and freely, with the closest thing to contraception they use being infanticide, which is far from ideal.
Particularly when animals are in oestrus or in season, they seem to be very keen on the whole reproduction business. We can never know for sure whether they understand how pregnancy works (though I doubt it) and whether they want that to happen, or if it’s just an instinctual drive. Either way, with the relatively high fertility rate of most species, they do a pretty good job at achieving pregnancy most of the time.
You have to understand a concept before you can have an opinion on it either way, and I honestly think most species just don’t.
And I am perfectly aware that somebody will try to jump on this post with “Forced pregnancy is rape” as an argument, and while forced pregnancy is potentially torture for a human, an Artificial Insemination really can’t be compared to rape. Rape is an act of violence. AI is a fairly minor husbandry procedure. You would do a disservice to humans who had experienced either to claim the two are the same.
It’s probably also worth mentioning that pregnancy and birth are a lot less trouble for most animals than they are for humans. Humans have one very large baby, most animals (esp. most domestic animals) have a number of small babies, making childbirth a lot less damaging. Animals are also a lot more functional during pregnancy than humans are in the later stages.