“Is it bad to leave a loose tooth in your mouth?”

You should find out why the tooth is loose and get appropriate treatment to stabilize the tooth until it is no longer mobile. failure to get treatment will eventually lead to the loss of the tooth as well as endanger adjacent teeth

Yes

I have not seen your radiograph nor have I examined your tooth, for the most part a tooth that is loose has lost a lot of bone support. If there is an opposing tooth in the other arch, every time you close, it's hitting against that loose tooth, and by rocking it, you are losing more bone, creating a deeper bone loss. If you ever want to replace that area, there will be a deeper void. It can also retain food particles and get gum disease (if you don't have it already). By all means, see a dentist, consult him, and most likely get that loose tooth out.

If it is a loose baby tooth there is no problem in waiting for it to fall out unless it is causing the adult tooth below to erupt out of line. If it is a loose adult tooth you should see the dentist right away.

It is always best to keep your own teeth rather than dental implants. Having said that, depending on how loose your tooth is, it is a great idea. You should see your dentist to get an X-ray and evaluation, if your tooth is infected or have enough bone to salvage it! Most loose teeth are due to gum disease or bite issues. For more info on gum disease and treatment, click here:
https://celebritydentist.com/periodontal-disease/