>Mice are so easy to keep, they could be entitely mechanicly reared, and an experiment involving 1000 mice should be a simple matter of a few clicks on a computer.

I invite you to go visit a laboratory that works with rodent models for a few days and see if you still think this is true. I would love to be proven wrong, but in my experience animal experiments are as non-automatable as human clinical trials. As a simple example, in my PhD I spent months injecting mice with cancer cells, measuring the tumor outgrowth, then harvesting the tumors, grinding them up and sequencing them. You can see the schematics of some of those experiments in one of my manuscripts (https://elifesciences.org/articles/41090 -- free to access). Each one of those experiments relied on dozens of different techniques (from cloning to making viruses to culturing cells to animal husbandry), most of which are not easy to automate because they vary from experiment to experiment. For instance, just to grow the cells for injection into animals, you need to monitor plates of cells growing in a sealed 37º incubator, wash and re-feed them as necessary over a period of days to weeks. Then, on the day of injection, you need to wash and spin them down, resuspend in an injection solution, put them on ice, go down to the mouse house, shave the mice, anesthetize them and then inject them. You don't want too much time to elapse between when you prep the cells and when you inject them or they might die. At every step there are biosafety constraints that limit your movements and how you dispose of garbage which would be challenging to scale up to a totally automated system. Every different cell line/type you inject has different kind of growth requirements and idiosyncrasies in how they like to be handled. I suppose you could program machines to do this for one cell line, but it would be a monumentally difficult task to do it for every cell line and get good results. Then there's the matter of just handling the animals. I would love to see a machine that could do this (and maybe one day there will be) but for the moment you need training in how to carefully and safely grab mice, restrain them, inject them and so on.

The costs of maintaining mice is also much larger than it seems (perhaps compared to mice kept as pets). A major cost is the daily tasks associated with husbandry, like cleaning cages, sick checks, genotyping, etc. At least at my institute it was ~$1.50 per day per cage (up to 5 mice) in support costs, not including the ~$30-50 it costs to raise a wild-type mouse to the point where you could do the experiment (more for some genetically modified mice). An experiment with 500 mice (100 x 5 conditions) would cost you $15-20k, which would massively balloon the cost of research.

Finally, there are major ethical concerns with using more animals than necessary for any experiment. Animal work is carefully regulated by internal and external ethics committees and oversight of all ongoing experiments. The number of animals to be used for any given project must be justified with statistical analysis suggesting that you are using no more than necessary and will indeed be able to show the expected results. If you propose experiments using large numbers of animals you must have a good explanation for why you need such numbers.

Anyway, it's not really that simple or cheap to do animal experiments, especially at large scale.