And I strip Exif data, too, intentionally, for similar reasons.

That makes sense to me for any image you want to share publicly, but for private images having the location and capture time embedded in the image is incredibly useful.

If you are uploading it to a website you are sharing it. Even if the image is supposedly "private" you have to assume it will be leaked at some point. Remember, the cloud is just someone else's computer, and they can do what they want with their computer. They may also not be entirely competent at their job.

Yes, once something has been shared (or stolen), you lost control over it, be it information or an image. EXIF data is fine, if it never leaves your device or if your device is not compromised.

If by private you mean "never shared", I agree.

That reminds me when I first uploaded a picture to some forum and it showed my full home address together with a map as a "feature"

It is a feature because now you are aware of what you are sharing and can potentially delete it before too many others see it.