Well, you actually want the body to clear things. That’s not a problem, it’s a feature. If the phage is able to target the bacteria before it is fully cleared, that’s all you need. Humans have been injected with phages and it has been shown to work. The Soviets actually did a lot of research on it, IIRC. The practical issue that is really challenging for broad phage therapy adoption is that phages are very specific to the bacteria they target. So, you can’t just get injected with any old phage and expect it to work. Instead, you need to catalog all the phages you find in a database and search for one that can target the specific bacteria the patient has been infected with. Phages are simply viruses that target bacteria. You’re awash in them all the time.