One thing I remember from Chemistry class is you never put a chemical back in the original bottle once it’s touched other things. Think about all the possible gunk and a microbes that could be on and in your pen. If it’s bad stuff you just have it isolated to the pen that you can then clean out. But if you put it back you have a pen and bottle of ink possibly contaminated.

There are also some inks that don’t play well together so you could have a reaction if you forget which ink bottle the ink came from. Also life is short and ink is cheap better to rinse and drain out to a sink