So, this is actually something I studied. A lot.
Rodents in the wild, particularly mice, inbreed very regularly. How laboratory strains of mice are created are actually by doing brother/sister pairings, after 20 generations, the mice are genetic clones of each other, giving you identical mouse after identical mouse to study - there are no variables in the strain, there are only the variables you introduce.
Does this mean the mice are healthy? No.
It means if you want to study mice who will ALL get a certain type of cancer at 3 months old and see if diet or another environmental factor can push that back to 4 months, you can.
If you want to test drugs to treat diabetes, there are strains of mice who are guaranteed to develop diabetes.
Can you take any mouse litter and get 20 generations and have them all be clones of each other? No again, plenty of developing strains fail before they get to that point because you’re locking in too many issues
So basically, while yes, it can be done … sometimes. And it can even, occasionally, be done indefinitely, you are far from being guaranteed any sort of healthy result. Linebreeding, carefully used, is an excellent tool for locking in good traits. But without some serious long-term commitment and a LOT of knowledge, you’re very likely to lock in bad traits as well; color you can see at hatch, a greatly increased susceptibility to mites or a strong tendency to develop digestive issues before they’re 10 is nowhere near as visible, but you don’t know you haven’t locked that down even tighter than the color.
Jackson Labs is the premier reference to study such things, they even offer a course; Common Laboratory Mouse Strains: A Beginner's Guide
And here you can see some commonly available strains with their strengths and weaknesses listed; https://www.research.uky.edu/uploads/commonly-used-mouse-strains
So anyway, hope no one minds the thread drift too much, it’s just, I really do study genetics a lot, I breed and care for a LOT of animals, I’ve carefully linebred some animals pretty tightly, I’ve got a couple of horses with only 1 grandpa so, while my opinion is only my opinion, it’s a pretty educated opinion, and I’m going to stick with “for something as common as a simple recessive you can buy easily, don’t breed brother and sister.”
Not that it sounds like rachaell has that scenario anyway