"The result of having all these unhealthy thoughts come into your mind while you meditate,"
I would hesitate to call these thoughts unhealthy, on the contrary they are completely natural and harmless. It is our reaction to those thoughts that can be unhealthy.
There is one reason that I can think of for why they would be classified as unhealthy - they distract you from what is happening right now and, as a result, you might miss something important. Multitasking is widely recognised as being a counter-productive activity. Do one thing at a time, with your full attention, and you will excel. Do many things at once and you will do all of them badly. Or one could say that multitasking is the process of failing at many things simultaneously.
I absolutely agree that you should focus on one thing, what I am saying is that meditation is training for that focus. Instead of forcing the thoughts out of your mind you just let them float and they disappear by themselves. But if you start seeing your thoughts as enemies and having power over you, you are losing ground.
I would hesitate to call these thoughts unhealthy, on the contrary they are completely natural and harmless. It is our reaction to those thoughts that can be unhealthy.