I'll just make a short list of the negatives of having a Parasite.
1.
No Privacy, EVER.
Think of the last person that you've spoken to, now imagine them permanently grafted onto your body. I don't care who it is you're thinking of, that is a terrible fate that introduces all sorts of complications in your life. You might get lucky and have a good relationship with your Parasite, but there will inevitably be a time where you just need to be alone, and you can't do that with a Parasite. Imagine the awkwardness of a simple trip to the bathroom. Imagine trying to have a relationship when there's another person living on your head.
This is probably the worst side effect of Parasitism
2.
It's going to change your body.
Regardless of how the Parasite is connected to the Host, changes in your body are going to occur.
Just look at Pre-Samson Filia, she looks pretty different doesn't she? You really have no say about what's going to happen to you upon attachment. I don't know about you, but I don't want a dragon speared through my brain or my skin replaced with an intestinal tract.
3.
A Parasite is a person.
You might be lucky and get someone polite like Leviathan, but what happens if you get someone like Samson? Parasites aren't pets, they're people with their own wants and needs. When you're the Host, the subjugated member of the relationship, you are at the mercy of the Parasite and it's whim. It's implied that any Parasite can take over as the main body, putting the Host in a coma like state. I would assume Parasites normally don't do this because it's such a horrible thing to do, but it's still scary to think that you're never really free.
As for your second question I would say that they couldn't because the very definition of a Host is that they get the short end of the stick in their relationship with a Parasite.
This is just my personal input, but I would absolutely hate to have a Parasite.